I also have hypothyroid. I was diagnosed at 25 y/o. It was during a time when I was working way, way too much, so I think the lack of sleep intensified the symptoms. I was nearly as tired as I am now that I'm a mom. :)
Anyway, like the previous response, the test isn't anything to worry about and the pills are also inexpensive - there should be a generic available. I have been taking them for 5 years now and definitely feel better. Also, since they will have you fast for the test, you may as well have your cholesterol, glucose levels, etc. checked. This also pointed me in a few directions to help address my fatigue. I looked into changing my diet. I know myself better than to think that I could go on a super strict diet, so I just eat well when I can, but don't punish myself when I can't. The doctors also told me to get more rest and exercise (I was single at the time, so that seemed doable). However, things like "rest" and even "exercise" are hard for moms, so I think with a little medication and maybe a reevaluation of diet, it will help. Also, it took me about a year to feel close to my old self again, so be patient and don't be discouraged!