Generally, if an animal bears NO weight on a leg, it makes me suspicous of a fracture (break). If there is a strain or sprain, or a puncture wound, then they usually will put some weight on it but may limp.
If Sammy is holding it right up off the ground, I would be thinking of a fracture. This could be a hairline fracture, such that there was minimal pain and no swelling.
You can read more here:http://www.petplace.com/cats/fracture-repair-in-cats/page1.aspx
I also want to mention that there are NO human pain killers or fever reducers that you would have at home that are safe to give a cat. Aspirin, acetaminophen (paracetamol) and ibuprofen are all very toxic to cats and should never be given! You can read more about them here:
Given that this has been a couple of days now, I would strongly recommend that you take Sammy in to see his family veterinarian to have him examined. He may need to have the leg splinted for a few weeks in order for it to mend.
I hope that this helps you to help this kitty!
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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 strongly advise contacting your regular veterinarian.