Since the thyroid produces hormones and since all hormones are connected if the thyroid is not working perfect doesn't matter what you'll do but your hormones are never going to be as they should.
Hypothyroidism because of Hashimoto is to be treated very differently since Hashimoto is an autoimmune disease causing your own immune system to recognize the thyroid as an "enemy" thus attacking it in the attempt to destroy it, of course this causes an hypothyroidism condition because the thyroid is maimed constantly.
In this case supplementing iodine is going to make things worst because iodine stimulates the thyroid which causes the immune system to get even more upset and aggressive against it.
I hope that since you have been diagnosticated with hypothyroidism an Hashimoto test has been carried out (is a blood test).
If you do suffer hypothyroidism but you don't have Hashimoto supplementing iodine is usually the best thing you can possibly do.
Iosol is a water soluble iodine by ammonium iodide, in other words provides both iodine and iodide, iodide is usually considered safer than iodine because of much lower toxicity.
The dosage of 1,8mg is not nearly high enough to elicit a response in a case like yours, this kind of dosage is more for general health purpose.
Iodoral is probably a better choice in order to provide both iodine and iodide (as potassium iodide), one tablet supplies 12,5mg of total elemental iodine (comparable to the average daily intake of this essential element by mainland Japanese), up to 4 tablets a day are recommended for hypothyroidism.
Compare the dosage you did use to those dosages and you'll understand no wonders you didn't feel much out of it.
Some doctors, like doctor Brownstein, recommend a supplement providing both iodine and iodide for hypothyroidism.
SSKI (potassium iodide) might work as well but maybe in order to normalize hypothyroidism Iodoral (which is a tablet form of Lugol's) or Lugol's solution (much cheaper) would be more effective.
It is not uncommon that supplementing even just one tablet of Iodoral (or the equivalent Lugol's solution) causes discomfort which is a clear sign of thyroid issues, discomfort will fade with use and much higher dosages become possible as thyroid gets better.