I agree that you may have several things going on.
The "simple blood test" suggested above is most likely TSH, which, by itself, is totally inadequate to diagnose thyroid issues.
To determine thyroid function, you need to get Free T3, Free T4 (NOT total T3 or total T4), TSH - these tests might confirm/rule out hypothyroidism; however, along with those, you need to get thyroid antibody tests, which would be Thyroid Peroxidase Antibodies (TPOab), Thyroglobulin Antibodies (TGab) and Thyroid Stimulating Immunoglobulin (TSI)...... These tests will confirm/rule out Hashimoto's Thyroiditis and/or Graves Disease.
All of the above tests *could* rule out (kinda, sorta, but not really) thyroid issues...... no, they wouldn't completely rule out thyroid issues, but would suggest that you might want to look in other directions, as well.
Have you had an ultra sound of your thyroid? Ultra sound/CT/MRI of affected lymph nodes?
I do agree that a mammogram might be in order, considering the lymph nodes in your arm pits.
What about a CBC or metabolic panel, that would indicate both red/white blood cell counts, along with other possibilites? Do you have recent cholesterol levels?......
Depending on tests already done, we might be able to suggest other helpful tests.........
Your symptoms sound like several different things going on. Your doctor should start running tests to rule out different diseases and pathologies.
For the thyroid, it is very easy to have your thyroid level checked with a simple blood test.
For the trembling and sweating..Are you diabetic? Your doctor should test you for diabetes or even low blood sugar.
For the swollen armpits...that sounds like your axiallary (armpit) lymph nodes are responding to an infection or inflammation. If you are female, you might want to have a mammogram to check for cancer. The mammo. will also show your lymph nodes in your armpits.
Sore neck......do you notice any swelling or lumps in your neck? Swollen lymph nodes in the neck can cause stiffness as well.
If you can't get your doctor to help you, then find another one who will.