I would feel terrible if I was taking as much iodine as you are and that is a plain fact. That amount for you may be way too much of a detox for your body to handle right now, or you may simply process it differently.
My brother in law has hep c, and guess what? The oil pulling, for a mere five mins made him violently ill for two days (and he never had any desire to return to it). If you have a toxic liver you WILL feel the brunt of the detoxification process doing something that makes many feel energetic without receiving the immediate noticable benefits others are touting. It would make perfect sense that to do large amounts of iodine if you already have this type of congestion would leave you tired and feeling like crap, and yes, the more of a toxic load you lay on the liver can definitely affect your energy levels and thyroid. Cutting back to one-two drops a day, increasing your water, salt, c, and maybe looking into liver and kidney support would be a better plan than jumping on meds. I am not sure if you took off regular time on the iodine each week or how long you have been on the iodine but taking a few days off a week or spacing your doses to every other day might help your energy levels. Be sure to keep on the cleansing aspect of the program even on your days 'off' from the iodine...your body will still be releasing toxins. Look into those footpads, they really helped me immensely. You can just get 10 nights worth to see if they help you. I am not sure what your history is, but it sure sounds like toxic overload to me.
Hate to see you despairing so, and the thyroid med is no quick fix if that is what you are hoping for. You might find a quicker result simply by focusing on helping your body move out the toxic load.
You know the biggest change for me with the thyroid (was diagnosed hypo 7 years ago and went off meds 6 years ago) was getting the heavy metals out, the difference in energy and metabolism were greatly affected by this long before I ever heard of iodine or oil pulling. It is possible since you are yanking metals out with both of these therapies you are experiencing a temporary overload of heavy metals circulating throughout your system -- if your liver is overwhelmed then you will not be able to properly convert the T3 or T4 (can't remember which one it is) no matter what you are putting in you because this is done IN the liver itself. Oil pulling is good because it helps get the bile flow up which in turn helps dump toxins from the liver, but your body, with the addition of iodine might be temporarily overwhelmed and what you are experiencing is a true detox in every meaning of the word. I would not leap on any bandwagons right now, I largely suspect that there are many readings any number of us would be getting right now that would only be a temporary state of affairs as the body is adjusting and cleansing.
I would, if you have not, recommend doing a good round (several months) on the gold detox footpads (you can get them numerous places, I use http://www.healthmarvels.net - they are fast, fresh and good in price.) The difference in ONE week with these in my energy levels was staggering. I still do them every now and again to help with heavy detox - they are an added goody to have to help clear things out when your system gets overwhelmed. If it is not heavy metal related they also work well for other things, and might help you through this phase.