How long have you has Hashimoto's and been on thyroid replacement? Many of us have Hashimoto's and it's really hard to tell when the thyroid is completely "dead", meaning it produces nothing on it's own. Typically, that's when we can stay on the same (or close to) dosage for long periods, with no symptoms.
What dosages of medications are you on (synthroid and cytomel)? And how long have you been on them? Have your levels been relatively stable?
It's customary to have to change dosages periodically, and remember that TSH is a pituitary hormone, not a thyroid hormone, and it often does not correlate with actual thyroid hormone levels. TSH also fluctuates greatly, even intra day. My TSH has been as high as 55 and as low as the current < 0.01.
Agree that you need to get the FT3 and FT4 levels tested and you probably do need an increase in medication. While it's customary to wait 3, 6, or even 12 months between blood tests when levels are stable, you should retest approximately 6 weeks after a dosage change, then again in 6 weeks, then if levels are stable, testing at 3 months could be in order.
If you have results for FT3 and FT4, please post them, if not, ask your doctor to do them and if he refuses, I agree that you should find another doctor, as this one will keep you ill.
Yes, that would explain having dry skin and being fatigued, I am surprised you don't have every symptom in the book, I noticed you mixed up your medications a little, Cytomel is T3 and Synthroid is T4, Has your MD done the Free T3 and Free T4 thyroid hormone tests? If not, I don't have to much respect for your MD, Without thyroid production, he should be checking your levels with these tests every six weeks not every three months, there was no reason at all to allow your levels to drop low enough to have a TSH that high. IF he has done these labs, please post them along with the reference ranges provided for each level, Ranges vary from lab to lab. If he has not doen these tests, then insist that he does, if he refuses, then you need to find another MD, as this one will keep you sick with symptoms when it is not necessary. Free T3 is the active hormone that your body functions on, and is the most important test for your hormone levels, and since you have no thyroid, Free T4 is impotant as well because this is like your storage hormone. Best Wishes FTB4