Can I Give My Dog Tylenol?

NO- you should never give Tylenol to a dog.  Aspirin is ok for intermittent short term use only.  If you can't figure out why your dog is limping take it to a vet.  A lot of times getting rid of pain for a dog can make the condition worse in that helius the leg if it don't hurt & rest is what will make it better most of the time. But I would definitely check for swelling, or any warm tender areas & go from there with it.  its unwise to give meds without knowing exactly where the problem lies

My dog had a accident  and was in pain, my vet offered to give him baby tylenol, so I gave him infant motrin, a little bit, after he started acting like a new dog, and he's only 8wks old.

I would like you to visit this one as reference and see the question Acetaminophen (Tylenol) safety in dogs,
but you must first of all let your dog checked by a doctor because
limping is serious. Instead of any self medication, Doctors should be
the first and urgent choice here.

Call your vet an ask before giving your pet anything. You never know what your dog can react badly towards. Especially if your dog is on any other medication. If anything I would suggest a bayer aspirin, crushed into his food. ( small amounts! )