I don't have direct experience with this but from my reading, most pain associated with Iodine supplementation is due to bromine detox. But it's rarely going to be severe enough to keep you in bed. I guess your thyroid could be taking it in and making you hyperthyroid, which can cause fibromyalgia-like symptoms like you have, as well as make you feel warm. This is supposedly only temporary as the thyroid adapts to its newfound riches.
One thing that might be helpful is to try to "push the buttons" in order to see what they do. You already know what happens when you push the "zero drops button", and now you know what happens (or has happened so far) when you push the "1 drop button." I wonder... what would happen if you pushed the "33 drops button"? 33 drops would get you the nice round figures of 50mg KI + 25mg I2. My thinking is that 1 drop is really not that much, and if you are detoxing, it's going to take years to get saturated on that dose. If your pain worsens on 33 drops, detox is a likely reason. If it improves, it could be your thyroid adapting.
If you're worried about severe pain (I wouldn't be), try it on a weekend. Be sure to keep up the salt loading and drink lots of water.