Could a painful pimple on the inside of the cheek indicate a tooth problem?

Possibly: Depending on the location of the "pimple", it could indicate a dental problem.

YES: If the pimple comes from the base of the tooth , and you see that the tooth is with caries or broken, yes. An x-ray is essential as to rule out an abscess coming from a tooth.

Doubtful: If the pimple is on the cheek as you state, I would be surprised if a tooth is involved. However since dentists are doctors of the mouth, it would make sense to see one to evaluate and treat appropriately

Definitely, yes: dental infection can cause "pimple" to occur in the cheek or on the gums. Also a broken tooth often has a sharp edge that may cut the cheek.