How to determine hypothyroidism?

Hypothyroidism runs in my family. (Father, paternal grandmother, aunt, etc all have it) I am 22 years old and a nurse. I am tired all the time no matter how much sleep I get. And I'm gaining weight but haven't changed my diet at all. I just want to feel more energized. Seeing as I work the nightshift it makes it pretty difficult. I know I need my tsh levels to be tested to determine if I have it, but how do I go about getting the lab work done? Do I just call my doctor and say, hey I think I have this, will you test me for it? I hate visiting the doctor and try to have as minimal interaction there as possible. Can someone give me some insight?