I had the same problem when they had me on synthroid. I went to a doctor on the armour thyroid list (which is real thyroid taken from an animal and not artifical thyroid cooked up in a lab). That made all the difference in the way I felt but was still to low to take care of all my symptoms.
I found an old time doctor who was in his 80s who said before synthroid, they always used armor thyroid and they always treated the symptoms. He said todays doctors look at one TSH number and try to use it to judge how much you need. But that the TSH system could be and probably is out of wack and the symptoms would tell you every time when you got the doseage correct.
So since my doctor won't increase my dosage, I carefully under took my meds (not recommending anyone do this, I just know my body and did this for myself. Don't need the burn from anyone who doesn't like this idea.) When he ran my blood test, he doubled my dosage.
I then took the amount he had originally prescribed. He ran the TSH again and the balance looked "in range and normal" to him. I then started to slowly increase the amount of armor thyroid I was taking until my symptoms began to subside. This increase in my dosage was done over a three month period.
Today, I feel great. I don't drag anymore. My hair is back. My mind is working like it use to. In fact, in all ways I am doing fine, except for that pesky TSH number.
A note: I am VERY, VERY careful to start to adjust my meds down about a month before my yearly TSH test is due. They run the test and it shows TSH is in the recommended "range". As soon as the test is run, I adjust them back up.
Good luck. Thyroid problems are very hard to work with.
Note: did you know you can paint a quarter size amount of iodine on your arm and your body will absorb the iodine which can help your thyroid. Also, many test they run today inject iodine and are the cause of thyroid abnormalities in the first place. Whatever you do, synthroid, iodine, armor thyroid, after test that use iodine, etc....drink tons of water as all that stuff gathers in the kidneys and can do MAJOR damage if you don't flush it out.