If I'm not mistaken, there are emotional support animals and service animals.

Getting an emotional support animal is fairly easy. See here: https://en.wikipedia.org/wiki/Emotional_support_animal

It'll allow you to keep your pet in your apartment. I don't know if you can take it in public places, though (except for parks and stuff like that). But, airlines let you take emotional support animals with you on a plane. (You don't have to put them in the undercarriage)

Service dogs are more difficult to get and they're expensive because they're specially trained. If all you want is a pet in your apartment, then I would just go for an emotional support animal. You don't have to pay to train them.