I have underactive shaking and take levothyroxine
.Thing is with thyroid levels if you are borderline they are loathe to prescribe because it can make you more hyper .They have to get the dosages correct .
They will probably moniter you to see how your levels are over a period of time .It took six months of tests before they decided I had thyroid problems and got me on medication.Hope they can sort you out and that you soon feel better ..
Have a look at the Bupa factsheet
Here