what kind of a doctor for thyroid?

An endocrinologist would be a specialist that handles thyroid problems - however, hypothyroidism (low thyroid function) is a common enough problem that the majority of cases are diagnosed and managed by internists/family doctors, so your regular doctor should be your first stop. If your case is particularly complicated, then he/she will refer you to an endocrinologist.

Your primary care physician. If it's the usual primary hypothyroidism, a family physician or primary care internists is more than capable. If you have some specialized problem, he can refer you to the appropriate consultant.

It's folly to run to subspecialists for common problems.

Endocrinologist.