Angry Cat

We just adopted a cat, and it turns out she was ill (severe ear infections, mouth ulcerations, URI etc.). She spent a lot of time growling and hissing in general when we got her, but figured she was just adjusting. After taking her to the vet, we've begun giving her her medicine ourselves, but she seems to be angry and now has started peeing on the carpet while looking directly at us.

We don't want to give her back, but we also can't have a cat that pees all over the place and hisses at us. Any suggestions or ideas on what we can try? I'm hoping this is just a phase but wanted to know if anyone else has experienced these problems and what has worked for them.

Yes, she has a clean litter box and is free of urinary issues. She gets along with the other cat we have. She does let us touch her, but at other times she runs away. 

One of the things you can do is buy Feliway spray and see if it works on her. If it does, I'd spray it daily and also get a Feliway plug-in diffuser(s). If the spray works on her, it should calm her down a lot immediately. Don't spray her with it, but spray stuff in every room daily.

Also, did you sequester her to only one room when you first got her? This usually helps new cats feel safe gradually. Then, when they're comfy in their safe room, they can be let out to be introduced to the rest of the place. Of course, some cats don't need sequestering at first but it sounds like many do.