Don't expect the "best answer" to necessarily come from your doc when it comes to thyroid disease. Many of us have been undiagnosed for years or even decades because of our doctors inability to figure this out.
See if your doc will run the correct labwork, even if your TSH is "normal". Your symptoms are classic hypo and many docs tend to disregard symptoms.
Ask for a free T3, free T4, TPO and TG antibodies, vitamin D, B12 and ferritin. If your doc refuses I'd look for one who will.