Re: OH Boy..
That's got hyper written all over it. You bneed to run more tests, particularly the T3. I had trouble with Synthroid as well where I was shaking like crazy and trembling all over. For me, my first doc never bothered to check my T3 and just went on my TSH number....turns out my T3 was borderline HIGH without meds and my TSH was HIGH too....after taking the meds, I went directly into Hyper land. Could very well be a sign of Hashi's.
You need to get rechecked before doing anything. Try calling the doctor to describe your symptoms and if you do not get the typical "its all in your mind" then stick with your doc. You need to get a TSH, Free T3, Free T4, Total T3 (less important), TOTAL T4 (Thyroxine) (less important) and if you can squeeze him to run both antibodies that would be helpful.
Some people just can't tolerate Synthroid/Levo. I was one of those.
That shakiness is a tremor...symptomatic of someone who is Hyperthyroid, not Hypo.
You should check your body temp to see if you are running above 98.6 degrees and check your pulse to see if it is higher than normal. Usually with Hyper, you will tend to get a few intermitent heart palpitations as well from time to time.
Keep us posted.