I am sorry your kitty is having trouble. Cats can pull muscles, and they can experience muscle spasms, but I do not think this is what is going on. I think that your kitty would be having this difficulty from the beginning if he had pulled something. I am worried that there may be some abscesses forming, or that there was some soft tissue or bony involvement. It is not good that a young cat does not want to jump, and I think that further investigation is needed. Another exam may be all that is necessary, or some pain medicines or anti-inflammatory medicines may make a world of difference. But, some x-rays may also be necessary. Injectable antibiotics are fine, but they do not last long enough to be of use. It is necessary for daily oral dosing, for a course of 7-21 days depending on the infection. And discomfort should always be addressed.
I do think another trip to the vet would be a good idea if you are able. Please let me know if I can be of further assistance. If this has been helpful, please hit the green accept button. Best of luck with your kitty!!