
Coway
Airmega AP-1512HH Mighty
Durable, effective for allergens/odors, but loud on high.

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Austin Healthmate Jr. Worth the investment.
Have a Austin Jr for years, great but not cheap. Recently bought a Levoit Vital 200S-P for another part of the house, very good right out of the box...very happy with the purchase.
I love my Austin air. I have a Jr with HEPA and it’s so quiet.
If you are looking to filter primarily VOCs I would look into the AustinAir Healthmate line. They come with 15 lbs of activated carbon filters. Most regular air purifiers don’t have that much carbon in them that you will have to replace the whole filter much more quickly to work against VOCs.
We have an Austin Air Systems Healthmate that runs 24/7/365, and has done since 1998. No lie. We only switch it off to change the filter (every five years or so).
Get an AustinAir if you have the budget. (750 range, Great for odors + VOC's/allergies etc.) Alens are also good for odors/VOCs with their best filter. (Alen 45i 350). Winix, Coway, and Levoit all good brands in general as well, although none specialize in odor/VOC area, all have good all-around units. So I'm not sure which aspect your baby needs most, but if money is no object AustinAir apparently makes some of the best, esp for VOC's/odors. IQAir even has commercial type units for around 1,000. A good all-around robust, but affordable unit is the RIA Breezeguard as well, around 400. For best + priciest look into AustinAir + IQ Air Mid tier RIA Breezeguard, Alen (350-400 range) as well those 3 brands all have various sized units in different price ranges and power levels, some in that range too. (Winix, Coway, and Levoit. All good.) Also get bigger or more units than the the minimum specs, for better effect. Also a good idea to have one in each room, or at least in rooms your baby will be in a lot you will probably want to buy a small or medium unit for those rooms. (So those mentioned brands have lots of variety of small + medium units for 100-200 bucks.). I have 8x units in a large 1br apt. So 4x in living room, 1 kitchen, and 3 in bedroom. But inherited an old smelly carpet with 5x types of mold. And could not afford an expensive AustinAir or anything like that. So I have a few bigish/mid range units, like the RIA Breezeguard, Alen 45i, another brand in bedroom, and then medium sized ones like two Levoit 300s, + bunch more for complete coverage. So my air is crisp + clean now. I can tell the difference in the air immediately when the purifiers are off, and when I did not have enough coverage, but some people don't seem to detect these differences and don't notice the difference. So even if you don't notice much...it may have great effect for your baby. Anyway, it's a great idea, and your air will be infinitely better.
Unfortunately I don't. You mean from car exhaust and stuff ? What part of the city do you live in ? I'm right over the bridge in SJ and do notice some pockets of bad air there, which I figure might be factories or something ? But I haven't investigated. I'm just outside the edge of the city air where there is some parks and greenery here. Although when it's really bad in Philly it's not great here either at times. (Yellow from red) Anyway, just googling it seems the carbon pellets can maybe help with nitrogen dioxide but that "treated" carbon is even better. (Idk what that is.). But if the general premise is true then the same IQAir + Austin Air would be best to look into. I saw an IQAir filter....for 429 bucks. Filled up like 12 pounds of all kinds of different pellets, and it says good against various VOCs + related. I'd ask their customer service, for both, and you can also try posting it here as a new topic too. Also ch-cut filters might help (not sure though). As you can get them for 20-30 bucks. I have some in my closets. They convert molecules into something else which reduces odors. So apparently breaking down the nitrogen and dioxide makes it easier to then get rid of. So I'm not sure if the CH-cut things break it down, or just convert it etc. Also you can buy carbon pellets packs for I think around 12 bucks, not sure how long they last. But maybe you could put some in mesh bag, behind a fan or something, and then you have a DIY little carbon filter to help. Something like that. (Or In a coffee mug in various places ? But not as much air will pass through.) And I don't even notice any noise...it's like a nice background noise that I actually like. Like being in a car for a while and you dont notice the engine anymore. I only notice when I turn them off lol but I don't find them loud at all...I like it. (Maybe when I stand right next to one.) The Alen 45i is known for being quiet and energy efficient, the levoits are decent soundwise and energy efficient too. My only not-quiet one is really the big RIA in my kitchen...so no big deal. (I still don't find it loud though, even on 2nd from max.) In terms of a baby, if extreme quiet needed, you could try multiple smaller units, all on low, as most purifiers are quiet on low. But you need to pair a few of them up to get = CFM then in that case. (Also I find the low background noise helps me sleep + take naps....so if your baby not bothered by it ...prob a bonus...)
For VOC's + odors Austin Air is very good but you would need to pay about 750 (they might have a cheaper one ?). That's one of the best, and probably worth it for your health imo. As you aren't even sure what your triggers are possibly, you want to get something very good. So those have a very large filters packed with lots of carbon pellets that absorb odors + VOCs and the filters can last for a few years apparently. Next would be like an Alen 45i which I have, with their best filter. (400ish) And it comes with a lifetime warranty, if you stay in the filter replacement plan. (90 dollars best filter every 9 or 12 months, your choice.) I would suggest adding another unit from your bedroom at some point too, for best coverage. levoits make good affordable units. However units under 200ish won't do a whole lot vs odors + VOCs. They may have a thin carbon sheet and/or some pellets in the black part of the filter...but it's not going to be as much as bigger/better units. But normal purifier with white filters will be fine for everything else. Cat dander, particulates, (some) cat hair (you will still have to vacuum some car hair that lands on the floor but will help.) Point is I have 8 air purifiers in my apartment to correct an old moldy carpet I inherited here. Now my air is crisp and clean...but I could never afford an Austin Air so I got the mid-range Alen 45i and A mid-range RIA Breezeguard (400) combined with the two Levoit core 300s I already had (90) bucks...gives me pretty good coverage in my main living room. Then Ive added 3 more for bedroom various brands, 1 midsize, 1 affordable one, and 1 small one on nightstand. So...beat is to just spend the money and then the beat and get an Austin Air I would suggest. But you could also perhaps slowly add units over time until you have perfect air. But will take 2-3 medium or affordable units probably. Top brands for general purifiers that people like a lot are Winix, Coway and Levoit, they all have various size options, I love Levoits myself. But for odors and VOCs...and Austin Air is one of the best, 750 range (maybe a 500 range unit ?). There is even IQAir which is like 1,000. And then mid-range Alen 45i, RIA Breezeguard, and some pricier Levoits + those other brands might have units in that range with some adequate carbon filters. Like the Levoit Everest Air which is 450 ish I think. But Alens will probably be a little better for odors/VOCs and Austin Air even better. Any of those other purifiers can help with cat hair, dander, particles etc. but since you have allergy to VOCs...I suggest getting the best unit you can. As for sphinx cats oils I'm not sure what you mean but if it's not a physical particle that can be captured in the normal white part of a filter...then it is probably a VOC that needs to be absorbed by carbon/charcoal pellets. You can also buy carbon/charcoal pellets and carbon strips for like 12 bucks i think and try placing them around your space discretely perhaps. To help. But mainly a good purifier will do most of the work. And probably more than one. (For best coverage 1 in each room, can be small or medium one in bedroom etc.)

Coway
Airmega AP-1512HH Mighty
Durable, effective for allergens/odors, but loud on high.

Levoit
Vital 200S-P
Smart, effective dust/odor; some find replacement filters pricey.

Winix
5500-2
Budget king, durable; poor VOC removal, Plasmawave disliked.

Coway
Airmega Mighty
Durable, great for allergies/dust, responsive auto-fan.

Winix
5510 & 5520
Good value, durable, effective for pets; carbon filter issues.

Ranked #1
IKEA - UPPÅTVIND

Ranked #1
CleanAirKits - Corsi-Rosenthal Box

Ranked #1
Austin Air - Healthmate Plus

Ranked #1
Winix - 5500-2

Ranked #1
Coway - Airmega 400

Ranked #1
Coway - Airmega AP-1512HH Mighty