New cat troubles

Preface: Roommate (23M) and I (26M) got a second cat recently from a friend that couldn’t home her any more. The cat was eased in appropriately with our other cat the way that most professionals say to do it and they ended up not being best friends but the tolerated each other.

Fast forward to 3 months later and now our first younger cat wants to play but the new cat is very reclused and doesnt like that. She has started not eating, barely uses the litter box and throws up foodless bile atleast three times a day. She is drinking water and although she was an indoor cat desperately wants to be outside and when inside will hide under the couch.

Shes gotten angry at our first cat for wanting to play so much that now our first cat goes for a quick play bite at her just to mess with her.

I am at a loss of what to do at this point cause she just refuses to do anything. Im planning a vet visit soon and we are keeping the cats seperated when we are home but the still have full reign of the house when we are at work.

TL;DR: new cat is not eating and avoiding everyone which is making old cat antsy. What do I do