It sounds like the concern given your symptoms would be for hypothryroidism (too little thryoid hormone in the body). The most common symptoms associated with hypothyroidism include: Decreased sweating, cool skin, brittle hair, fatigue, shortness or breath, decreased ability to exercise, runny nose, decreased taste sensation, weight gain, carpal tunnel syndrome
and many others.
Because the function of thyroid hormone is so diffuse throughout the body, low or high thyroid levels can affect almost every organ system and the clinical manifestations are widely varied. However, the test for low thyroid levels is a simple blood test and it seems your constellation of symptoms more than warrants an evaluation. I recommend that you seek a second opinion
from another health care provider if your doctor
is unwilling to complete the brief evaluation for thyroid disorders. This is especially reasonable in light of the fact that low thyroid hormone can be a signal of other medical conditions that may also need to be workup up further. Additionally, the treatment of low thyroid is very simple and inexpensive as there now exists a synthetic form of human thyroid hormone. This treatment is available in a pill form with once daily dosing.
I hope this helps!