I agree it wouldn't hurt to make sure he doesn't have a UTI. Beyond that, you mention you walk him 2-3 times a day. Are these the only times he has an opportunity to potty outdoors? If so, I would take him out more often. As a tiny dog he may not have the storage capacity of the Rotties you are accustomed to.
I would retrain him as though he was a puppy. He might simply be kind of clueless. Some dogs need a bit of help generalizing that they should never pee anyplace where they can look up and see a ceiling. Take him out every hour, reward him with a tasty treat and praise when he pees outside. Inside he should either be under close supervision (that is, sitting in your lap or actively playing with you) or else in his play pen until you are ready for the next potty trip. Space the potty breaks further apart once he proves he can go a full hour without mishaps, then a full 90 minutes, then two hours.
I would retrain him as though he was a puppy. He might simply be kind of clueless. Some dogs need a bit of help generalizing that they should never pee anyplace where they can look up and see a ceiling. Take him out every hour, reward him with a tasty treat and praise when he pees outside. Inside he should either be under close supervision (that is, sitting in your lap or actively playing with you) or else in his play pen until you are ready for the next potty trip. Space the potty breaks further apart once he proves he can go a full hour without mishaps, then a full 90 minutes, then two hours.