It’s acetone, not ammonia. The acetone needs to evaporate in order for your nail polish to set.

Your best option will be gel polish. It cures under a UV light and is completely dry and odorless once it’s cured. Depending on how quickly your nails grow, gel polish can last a decent couple/few weeks. Downside is that it’s a pain in the ass to remove and can damage your nails if they’re fragile.

You could also try press-ons. I haven’t tried them since the mid-nineties so I can’t personally speak to the quality or longevity, but they’ve had a resurgence in popularity lately which makes me think they’ve gotten much better.

If you stick to regular nail polish, you could try a few things:

• Work in thin coats - thick polish takes too long to dry.
• Quick-dry polish and/or quick-dry topcoat. A lot of people like the Seche Vite topcoat because it dries to the touch in like 5 minutes, and sets pretty well after about 2 hours. Be warned though that it often causes shrinkage, so be sure you wrap your tips and leave less of a gap around the cuticle to help reduce this.
• Use a hairdryer on warm to make your polish dry more quickly.
• Once your nails have dried to the touch, gently wash your hands (pat them dry rather than rub them with a towel).
• Pet your cats from behind so they don’t get a whiff of your nails.

Vaya con dios