"Is it absolutely neccessary to see a doctor or get tests on my thyroid before I start taking Iodine?"
You seem to be in the best position to answer this question. Get a glass of water and put a drop of the Lugol's in it, mix and drink it down. Then, see if the question is answered. :)
A tiny percentage of people show an adverse reaction , be aware of that, search this forum, learn. Or else just go get a test.