Hi and welcome! Your Free t3 and Free t4 are what really count and those were not tested. These are probably low and this is why your TSH is so high. The pituitary gland puts out TSH in response to where your "frees" are.
Most people feel at their best when the Free #'s are in the upper quadrant of the reference ranges.
As far as the meds go, give it some time. It can take anywhere from 4-6 weeks to balance out. If you start having more adverse affects, the doctor could prescribe a different t4 drug like Levoxyl. And then there's the natural route, Armour. Many people do wonderful on Armour but good luck getting a doc to rx it.
May I suggest something to you? Keep a journal every day of the meds you're taking (or if you forgot to take them), your basal body temp and your symptoms as well as all of your labs (ranges and dates too). This can be very benificial for you and your treatment. You won't have to do it forever, just until you're leveled out and feeling well.
Take care and again, welcome!
[edited to fix typos