The only thing I can think to add regards the Lugol's versus SSKI. Getting that iodine converted to iodide might lighten your load. Since you have 15% Lugol's, that sounds like maybe you're not in the U.S.? If you don't have easy access to either SSKI or potassium iodide crystals to make SSKI (there are easy instructions), consider taking your Lugol's with the vit C. See if that helps your tolerance. Best wishes!
Edit - I was slow typing, and your other response was posted before I finished :) If you can get SSKI in the UK, great. Take that instead of Lugol's, till you're feeling more confident. If you can't get SSKI, use the vit C crystals to convert the iodine to iodide.