I had a doctor just like that. I don't have him anymore.
When he wouldn't diagnose what I knew to be hypoT, I took myself to an endo who was smart enough to know what it looks like when she sees it. (Not all endos do, though; I got lucky on only one try.) She gave me my diagnosis but wouldn't treat it with anything but Synthroid, which didn't agree with me. I had to see a third doc to get the right thyroid med for me.
You know in your heart what's wrong with you. I did too. Had to pursue it with more than one MD, though, and you may have to as well. HMOs are the pits, and I'm not sure what to tell you about coping with one. Isn't there an appeals process of some sort? If you truly have no choice, you'll have to try reasoning with the Immovable One. Ask her to humor you. Emphasize the family history. Point out how your FT4 is scraping the very bottom of its range. Tell her that you know that healthy people have TSH around 1, no higher than 2 (even if you didn't know before now). Ask for a 50 mcg trial of thyroid hormone to see if it helps with symptoms.
Ask - rather, insist
- on thyroid antibodies tests, both TPO and Tg. Positive AB tests are enough to push some MDs into action. If she still won't budge, she's too stupid for words and doesn't deserve your business. Do whatever you have to do to get a consultation with someone else.
From what I know, the low ferritin is a common concomitant condition with hypoT, but it will still have to be treated with an iron supplement. I don't think treating the hypoT will reverse that without taking extra iron for a while... At least, until your periods become less heavy after optimal thyroid treatment!