Kitten changes limp please help new kitty owner

Hi there.
I adopted an 8 week old kitten from the humane society on Friday. He is so relaxed and well adjusted. We also have two small dogs. One adores him and the other just ignores him.
His name is Binion, we call him Binny.
He has been to our local vet twice. First on Monday and again yesterday, Wednesday.
When we went Monday he was in tip top shape. Except he has soft bowel movements that stank something horrible. His fecal lab showed nothing so perhaps it was the change in his food.
We went back to the vet on Wednesday because he acquired a limp in the front leg. Upon examination he showed no signs of pain. But the vet saw there was a definite limp and suggested if it didn't seem better today to come in for an exray.
This morning he didn't show a limp, just a little stiff walking perhaps.
He has spent much of today sleeping in the pet bed which we keep warmed with a heat disk under some blankets.
When I got him up by putting food in his dish for dinner he has a very obvious limp however when we watched him, the limp now seems to be in the rear leg.
He went from being non stop playful to limpy and sore and just not feeling well though he is still happy to eat as well as purr and pretend nurse on my neck.
And so I post here.
I had asked my vet if this might be the limping kitten syndrome as I read about it online but he said no because it is rare and Binny isn't showing signs of respitory issues.
I would appreciate some input from actual pet owners. I trust my vet but my gut instinct is that this is limping syndrome and I'd love some input.
Thanks
Wendy and worried husband Shannon

He could've hurt it playing and it might just be something similar to a sprain.  Did the vet do a stool sample to rule out parasites for the runny poops?

Yes he did the stool sample and said it was clean.
I was reading our adoption papers and he got the FVRCP killed vaccine on the 14th. My guess from what I have been reading online is this is a reaction to that, the limping and tiredness. It said they can have a reaction up to 3 weeks later and the calici in the FVRCP can cause the limping and sleepiness. It said it should clear up in 2 to 4 days, right now we are a day and a half into it. Since he still has a healthy appetite and is drinking well I think we will continue to watch him and hope he is on the mend by weekend.

I almost mentioned the calici virus because of the limping.  You might want to mention this to the vet just to know for the future.  He may not be able to have the next round of vaccines if he reacts.  The vet can order the individual vaccines if needed.

I will mention it for sure! He doesn't think it is a reaction because there are no upper respitory symptoms but I really feel like it is. I will tell him for sure. Thanks!