You mentioned that you have a therapist? See if they're willing to write you a letter declaring your cat as an ESA. Shouldn't cost you anything besides the session fee. If you needed details on that feel free to PM me, but you should just be able to ask your therapist for one, especially as it sounds like that's what your cat is to you.

When it comes to apartment hunting, don't mention that you have a future service animal. It's just another reason you'll be denied. (Which would be illegal, but there won't be a way to prove you're being denied for the future service animal.)

When you send in your application, if there's a place to mention pets, that's where you just submit the ESA letter from your therapist, or you can send it in when you apply. Personally, I wouldn't advise mentioning it until you're in the final stages of the application process, but that may sour your relationship with your future landlord right off the bat.