You can be hypothyroid and skinny. Have a look at this table of symptoms

http://www.drrind.com/scorecardmatrix.asp

It possibly means you have more adrenal problems than thyroid. It would also account for the nervousness and inability to put on weight.

Iodine is a bit of an unknown when it comes to treating thyroid. Works well for some, not for others. I would get your adrenals tested first, to see if you can tolerate thyroid treatment.

Best
Nicola