It would not hurt to get a second opinion.
A good doctor would look at your numbers but ALSO take into account your symptoms and your discomfort.
Going strictly by the numbers often makes hyper and hypo thyroid patients miserable.
Graves disease can have complications especially with your eyes and heart, and it can also make you jittery, nervous, restless and stressed.
There are 3 recommended treatments for hyperthyroid:
Drug treatment with anti-thyroid drugs
Ablation of the thyroid gland with Radioactive Iodine (RAI)
Surgery to remove all or part of the thyroid
The anti-thyroid drugs work well in some people but not in others.
It's a good non permanent first thing to try.
Many people don't like the Radioactive Iodine method.
Seeing as you have a cyst, a partial removal of a portion of your thyroid might be a good answer for you.
http://thyroid.about.com/od/thyroiddrugstreatments/a/thyr...
Additional:
You can try finding an endocrinologist but in some areas it is hard to find a good doctor who is willing to work WITH you.
I had a great doctor for many years, an internist, and then we had to move away from the area and I had a difficult time finding a new doctor.
I interviewed no less than 6 of them before finding one that would work with me.
He is a general practitioner.
I've been hypothyroid for 18 years, have tried Synthroid for many years and have found that Armour Thyroid works best for me and I had a hard time finding a new doctor that would prescribe Armour Thyroid.
Besides checking my blood work every year to set my prescription, we have a long chat about how I feel, is my skin and hair alright, do I have any heart palpitations, have I had any problems, etc.
I found my optimal prescription level and I feel best when my numbers indicate I'm right on the edge of being hyperthyroid - the comfort level is very individual and it's different for everyone.
Finding a good doctor can make a world of difference, but it can be hard to do.