My name is***** have been a veterinarian for 11 years. I am sorry to hear that your cat is limping. I hope I can help you with your question this evening, I do apologize for the delay in getting you a response.
The first step is to look at the paw/leg for any injuries, such as swelling, punctures, or heat. The most common cause of lameness in cats is puncture wounds from bites (from other cats is most common). The second most common cause is trauma resulting in muscle strain/sprain or fracture of the bone.
If you are at risk for getting bit by your cat, then please stop touching him.
Unfortunately, he will likely need to see your primary care veterinarian to treat the problem (antibiotics and cleaning the wound if there is one, as cats abscess very easily) or dealing with whatever is going on.
Until you are able to get into the veterinarian, I would recommend keeping him confined to a small room, or perhaps a large dog kennel, where you can keep a litter box, bed, food, and water for him. This will prevent him from using his leg excessively and potentially straining another leg.
If you have any additional questions or would like further explanation on anything I have shared, please let me know. If I have answered your question completely, please take a moment to rate me so that I may continue to provide and improve my services.