I only know the doctors options; if they find something, like cancerous tissue; it is to cut it away or radiate, or medicate. The first two would reduce the swelling. The latter I am not sure the outcome of.
If to do this myself I would adress the swelling, inflammation more than a thyroid issue. Like if you have a swelling of the knee, or elbow, would you cut it away or work on it.
Loads of options in addition to iodine:)