Abnormal hair shedding is linked to both low ferritin and thyroid related issues.
It's common for thyroid problems to arise after hormonal changes within the body eg: puberty, pregnancy and menopause.
I'm glad you are on thyroid med's but they ought to be checking your Free T3, Free T4 and Thyroid Antibodies just incase you have a thyroid auto immune disease eg: Hashimoto's or Graves and some people can have both.
For now, give your thyroid meds a chance to kick in, it can take 4 - 6 weeks to see any changes. Just be careful not to take any other vitamins/supplements etc too close to your thyroid meds. Usually it's advised to wait 4 hrs before taking other supplements.
You can get much more information and assistance on the thyroid section of the Healthboards. If you still feel unwell and your doctor wont assist you further then don't be afraid to find a new doctor. Make sure you keep copies of ALL your test results so you can take them to a new doctor if need be and to get help off the boards.
Keep taking the iron supplements and sometimes it can take a little while for ferritin to rebuild iron stores in the body.
Lastly, get another blood test to check your Vitamin D and B12 levels if you can. Low Vitamin D in particular is often linked to thyroid issues as is low ferritin. All these things need to be at the high end of the lab range.
You will need to be patient, but good luck and i hope you feel better soon