Synthroid may be the wrong med for you, not all meds are created equal and your body may not be responding to synthroid. Ask for a brand change and see what happens, keep in mind it may take a while to find the one that works for you.
I have a friend that was on synthroid and she lost hair and gained weight, she switched to another brand and is doing better, also I had a lab tech tell me once when I had bloodwork done that synthroid makes you loose more hair, and I have heard others say the same. Some will say no, meds don't do that, but too many people I have heard of have had that happen on synthroid, so I think there is a connection, it may have to do with ones body and how you react to the chemicals in the meds, it doesn't affect everone the same.
Also, I have heard that if you do not feel a change in symptoms after being on a certain med for a while than you need to try another because that one is not right for you.
Ask for another brand of med, see if that helps, if the doc refuses, get a new doc.
Good luck and keep us posted.