Hair loss can be caused by excess inflammation and certain matrix metalloproteases, as well as the accompanying hormonal imbalances. Most inflammation starts in the intestinal tract, so that's where I'd start. Candida can increase MMPs and inflammation. You may have limited success with thyroid supplements when there is ongoing inflammation and other hormone issues.
The nail ridges can be from stress and adrenal imbalances which go hand-in-hand with thyroid issues.
Low iron and ferritin levels can signal hypochorhydria (low stomach acid), another problem associated with candida and intestinal inflammation. Good stomach acid is necessary for proper absorption of iodine for nomrla thyroid function.
All the supplements are good, but may not be very effective in the presence of systemic candida, intestinal flora imbalance, and ongoing inflammation. I would start with the McCombs Plan to reverse the effects of the antibiotics.
A good shower filter can help reduce exposure to chlorine and other chemicals that affect health cells and tissues.