What test was actually done? Was it TSH? That's usually the first test primary doctors order. Is that the only test she ordered? What about Free T4 and Free T3? Those are the actual thyroid hormones, whereas TSH is a pituitary hormone and doesn't tell the whole story.
Typically, with hypothyroidism, we expect TSH to be higher since it's counter-intuitive - when thyroid hormones are low TSH is high because the pituitary is trying to stimulate the thyroid to produce more thyroid hormones and when thyroid hormones are high TSH is very low because the pituitary is trying to get the thyroid to stop producing hormones.
In your case, unfortunately, your doctor is right - your TSH is, what is considered "pristine"... but since TSH is only a small part of the picture, you're a long way from getting any kind of diagnosis...
If you can get her to order Free T4 and Free T3, that would be a help. If those are low, along with the low TSH, that would indicate that you have Secondary, otherwise known as Central hypothyroidism. With Secondary hypothyroidism, the thyroid actually works fine, but there's a problem with the hypothalamus or pituitary glands in which there isn't enough TSH to adequately stimulate the thyroid to produce thyroid hormones.
You can mention Secondary/Central hypothyroidism and the importance of testing Free T4 and Free T3...
Is tiredness and lack of energy the only symptom you have? Because of the tiredness/fatigue, it would be good if you could get tested for vitamin B-12. B-12 deficiency causes the most horrendous tiredness you can imagine. I was diagnosed with pernicious anemia (one cause of B-12 deficiency) long before I was diagnosed with hypothyroidism and before I was started on my B-12 shots, I was so tired I could barely drive home from work most days. One day, I actually fell asleep on the way home and don't remember driving about 1 block... That was terribly scary and I called my doctor right away to tell him something horrible was wrong. It still took months before they found the problem.
You should also get tested for ferritin, which is the iron storage hormone. Iron deficiency can also cause extreme tiredness. Iron is also necessary for production and metabolism of thyroid hormones.
If your doctor refuses to order further testing, you really should think about seeing a different doctor in order to get the proper treatment.