pmcgall,
As you may have read in my reply to you about tweaking, I had anxiety with adjusting to thyroid medication and in my case, once I was adjusted, I never had the anxiety with dose changes again. That was a nice change because anxiety is a terrible symptom to deal with! I especially hated experiencing it when I was out in public and this too seldom happens anymore and only mildly when it does.
My opinion is that for a while, the thyroid med and the thyroid itself, kind of battle for control of your body. The medication suppresses your thyroid and over time it begins to atrophy (accept its own death). During this transition, even mild fluctuations can cause the anxiety symptoms.
The as-needed anxiety med is a good idea but I'm sure your Dr. mentioned that continuous use of it for extended periods of time, like for more than two months can cause dependency. There's less chance of dependency when you don't take it every day but maybe two or three times a week and if you don't need whole pills, you can try cutting them in half. I only mention this because it allows use of them for more extended periods of time with less chance of dependency.
Chances are, your body will adjust to the thyroid med more as weeks go by and you may seldom need the Xanax afterward. If you do need it at times however, don't feel ashamed or embarrased because you do what you have to for coping better.