Yes..your Gyno can test your tyroid. If it is something wrong,he or she can make a referment to a Doctor that is better equipped for you to see. Also much easier when a Doctor refers you another Doctor.
Not a dumb question. Your gyn or family doc can order the blood-test so if you already are going to see the doc for something else, or if you are just comfortable with that doc then go ahead and see them. The other issue is your insurance. My insurance allows me to see any doc I want without a referral. Since I have to take time out of my workday to see a doc I always just skip right to the specialist.
Dumb Question Here 
