I'm not sure if my puppy has had initial shots, if he has will it hurt him to have another or should I wait 4-6 weeks

I would talk to your vet.

How old is your puppy? Where did you get the puppy from? Why are you not aware of his vaccination history? The "breeder", and the fact that you have no vaccination history makes me use the term "breeder" with a bad taste in my mouth, should have supplied all of this information, including what sort of food he's eating, when you got the puppy at 8 weeks of age, or later, but not before 8 weeks.

I have a shih tzu puppy and not sure if he has had his distemper shot cause we got it from a pet shop and they didn't know .

Puppies require a set of 3 vaccinations, each a month apart. This is usually done at 8, 12, and 16 weeks. If the pet store did not provide proof of vaccines I would assume that the pup is not vaccinated, but check with your vet to see what they suggest.

I have a shih tzu puppy and not sure if he has had his distemper shot cause we got it from a pet shop and they didnt know .

If you bought your puppy from a pet store it's likely from a puppy mill. Puppy mills don't vaccinate their dogs. They barely feed them. They don't even provide basic care to these animals. Neither do pet stores. So it's safe to assume that your puppy hasn't had its required vaccinations.

But talk to your vet.

This.. and among many other reasons, is why you do not purchase a puppy from a pet store.

Take your puppy to the vet and ask for their advise. They will know the best vaccine protocol for your puppy and your situation.