Can losing weight or over exercising cause thyroid dysfunction?

Hypothyroidism is linked to both sides of my family (my mom, grandma and basically all my aunts suffer from it). Last May I got blood work done and found no issues with any TSH, T3 or T4 levels. I was 23 at the time. That September I set out to lose just 20 pounds to be at my ideal weight. Over the course of 5 months I was able to do so by good diet and exercising 1-2 hours 5 days a week (also, at this time I was taking one graduate course and working 40 hours a week). I was about 2 pounds shy of my goal weight and found myself EXHAUSTED and almost unable to function for over 2 weeks! I went to my PCP in February and she ran more tests and suddenly my Thyroid was way under-functioning and lacking mostly in T3 (less than 9 months since previous checkup). Since then I've been on synthroid and have gained over half of my weight back (I am too exhausted to keep up that workout regimen). I was just wondering if maybe I jump-started the onset of the disease by losing weight or overworking myself. Also, I'm hoping to find some tips for how to get back on track of weight loss now that my energy level and appetite is all out of whack due to this disease. :-/