I am hypothyroid and take both Synthroid and Cytomel. The cytomel helped a lot - although I had to persuade my doctor to prescribe it. There is an excellent thyroid site at www.about.com that has the entire New England Journal of Medicine article on the benefits of adding cytomel.
Any weight loss diet will result in a drop in thyroid function - if you are noticing increased hair loss and other symptoms, I would suggest you get your blood levels checked - you might need a medication revision.
The virgin coconut oil thing sounds intriguing. The sites I checked advised that the coconut oil be unrefined. This pure, unrefined oil seems a bit pricey, but I'm willing to give it a shot.