Hi there and thanks for your question. Sorry to hear that your girl is not well!
By far the most common reason for limping after a cat fight is infection. While sometimes we can see a visible wound, often we cannot. Cats carry a nasty bacteria on their teeth and claws that can cause very serious infections. She may have a cellulitis which is an infection in the muscle that is very painful.
Unfortunately it sounds like she will need to see the vet. These types of infections almost always need oral antibiotics in order to clear up. If we wait too long the infection can get worse and she may need to stay in the hospital on IV antibiotics.
The vet can do a good exam and if they suspect something more serious like a fracture may do xrays. They will likely also take her temperature. Most cats with cellulitis will have a fever as well. The fever is likely what is causing her to not want to eat. Again, it is important to have her seen soon because if cats go a few days without eating they can develop fatty liver which is very serious.
I hope she does ok!
I hope this information helps! I will be online for a short while more. So, if you have more concerns about this question you can just hit reply. However, my baby will be waking up from her nap soon and I will be offline after that. If that happens I will respond when I come online again. Or, if my answer has been sufficient, please hit accept. Thanks!
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would highly advise contacting your regular veterinarian.