There's really no test - anxiety is a symptom. They only thing I can suggest and hope for you - is that you and your doctor have a good patient/doctor relationship and he/she really understands the symptoms of thyroid disease.
Here are some sites you should visit and print out if necessary for your next visit.
http://thyroid.about.com/od/depressionanxiety/Depression_Anxiety_and_the_Connection_to_Thyroid_Disease.htm
http://panicdisorder.about.com/od/thyroiddisease/Thyroid_Disease_and_Anxiety_Disorders.htm (THIS IS A GOOD ONE)
http://thyroid.about.com/b/2005/07/16/anxiety-in-subclinical-thyroid-conditions.htm
http://adam.about.com/reports/Anxiety-disorders.htm
I will say the closer you get to euthyroid you should feel less antsy with anxiety. Best feel good TSH is between 1.0-1.5
The list is too huge - I have only given you a tiny snapshot of research.
Would the doctor know to test this type of stuff?
Anxiety is a symptom of thyroid disorders. Hormones can and mostly will chemically change for you and most develop anxiety in both hyper/hypo. Regular stress can be present too - but I believe the thyroid excelerates the anxiety.
Good Luck and watch your cholestorol levels. They should be maintain depending on how high you really are.
BTW im a 21 year old male