Is It Safe To Skip One Dose Of Synthroid Weekly, And Should I Still Be Testing T3 And T4 Along With TSH?

I am age 60 with HYPOTHROID AND HAVE BEEN ON SYNTHROID since age 34. I take 137 synthroid and my test results for thyroid test is 0.03. Is this normal? I have asked my Dr. for a referral to see an endocrinologist but she will not. She recommended skipping a day once a week. Also my previous Dr. Used to test not only for my TSH, but my T-4 and my T-3. Why and is it ok to just skip one dose per week?