I would do your best to get to an endo, but you do need to start with your primary care doc first. Your gyn may run the tests for you and that should be able to get you the referral you need. I would be sure to mention your symptoms and almost more importantly your family's history of not only hypothyroidism but Hashimoto's as well. If you have Hashi's it's essential that you see an endo who can help you with it (some for hypo, but moreso with Hashi's because the damage can happen over a period of time).
www.endocrineweb.com is a great place to start to familiarize yourself with the thyroid, the disorders, and Hashi's.
Let us know what happens,
Cynthia