Hi Da Rosa,
It could still be all sorts of things - don't get too fixed on one thing, but keep chasing your doc to keep investigating. Like you say, you've got a strong genetic link for hypothyroid. But it could be some sort of female hormone imbalance which could also make you put on weight. Or maybe something else we don't know about.
Buying thyroxine/armour and dosing yourself with nothing to base it on could be dangerous - it can cause heart attacks etc.
I know I'm prepared to buy thyroxine/armour if they won't renew my prescription, but I do have blood tests which show me to be hypothyroid and I have been on at least 50mcg under medical supervision - they just don't agree with the amount I've upped it to - and some docs in the practice dispute treating mild hypothyroid (goodness knows where they get their ideas from).
So - I think maybe you should find out what the numbers were from your tests and keep pushing them to find out exactly why you aren't having periods. It's not like you're anorexic, so that shouldn't be stopping them, you're eating sensibly. So there has to be a reason, they need to find it for you.
I think you need to go back and talk to them, assertively and calmly and say that you're not happy just being left to see if things get better, that its been a year now and you expect to be helped.
Good luck and let us know how you get on, take care, Jay