Tsh is 0.06. Two weeks later tested t3/4 which is normal but Tsh is now 0.05. Not taking any thyroid meds. Doc not concerned. Should I go to a endo?

Thyroid function. Normal T3/T4 with a suppressed TSH suggests that your thyroid is functioning autonomously. Often this can be due to a benign neoplasm, or possibly an autoimmune disorder. It bears further investigation, which as you suggest would be best undertaken by an endocrinologist.