I think i have hypothyroidism, but my doctor will only do a tsh level test and he says that it is normal. aren't there other tests that can be done?

Not really: if the TSh is normal the other tests will be fine, so he is doing the right thing. You need to discuss with your doctor why you think you are hypothyroid. is it your energy, sleep, hair falling out or what? The symptoms that concern you like maybe weight and energy levels might need to be addressed on their own merit

If symptoms: If you have symptoms of hypothyroidism, you may be right. If patients are symptomatic, a free T4 and sometimes a freeT3 will be low or low normal. Some people feel better when in mid normal or high normal range. Do you have constipation, cold intolerance, thinning hair, low energy or fatigue, abnormal periods, depressed mood, mild lower extremity swelling, etc? Sick euthyroid syndrome also treated

Hypothyroidism: If TSH is normal and you still suspect hypothyroidism then a T3, (liothyronine) T4 level may be indicated. Can check for euthyroid sick syndrome.

TSH is: usually adequate, however, there are patients with technically "normal" tsh's that aren't in an "appropriate" range for age. On some of those, a clinical trial of BRAND NAME T4 replacement may sometimes be attempted, but you need to have defined guidelines before initiating replacement. Make sure your free T4 has also been checked, If you have questions, see an endocrinologist.