Are there any ointments or pills you can give a dog for a sprained or sore muscle or tendon?

No ointments that I know of. Never give a dog any of the modern pain remedies, Tylenol, Ibuprofen, etc. You can give it aspirin, 5 mg per pound of dog every 8 hours, a regular 325 mg tablet for a 65 pound dog. Buffered aspirin is better for the dog's stomach. For smaller dogs, baby aspirin comes in smaller doses.

I have heard that pain killer can allow the dog to aggravate the injury.

Yes, I agree with labman. A sprain just has to heal on it's own. Buffered aspirin, at most, would be the only thing a vet would suggest. This kind of thing happens at least once in most dogs lives.