Welcome to the forum Joanne,
I am sorry I can't help with the skin products question. Being a man I don't use such things myself. But I know they have been discussed on the forum many times before so maybe a helpful person will come along soon with info.
Basic info regarding starting the gluten-free diet for you though:
Try to stick to whole foods cooked at home for several months at least. No eating out at friends or restaurants.
You may find it helpful to stop all dairy for a few months also.
Oats are a problem for some of us as well as wheat, rye and barley So it might be good to avoid oats also.
Your rash could be DH (dermatitis herpetiformis), which is a an itchy skin rash only people with celiac get.
Sometimes people starting the gluten-free diet think they will recover in a couple weeks. But it is more common for recovery to take months or years.
It would be wise to have your doctor check your vitamin and mineral levels for deficiencies.
You're asking some pretty impossible questions there AG. I can't tell the difference except if it's a glutting, then there will be some (for me) GI distress & an under eye tic on my right side & snoring for starters but these things come a couple-3 days after the fact. So right off the bat, I can't tell just by the rash. If days go by & I only have the rash, then I know it's iodine related.
Everyone is an individual. Remember that. MOST people do not have this go on for years AG, MOST, the vast majority, are fine in months to a year. You keep going like this & you're going to make yourself sick. You're stressing. Stress can make the rash flare. Stress can make the rash flare just like ODing on iodine. Chill out some friend. OK?
Don't get me wrong. I understand the need to know what you're up against, I understand research, but one can overdo it & make yourself crazy. I've been there. I am only speaking in an effort to help.
I never get them on my palms, thankfully; only on the sides of my fingers and occasionally the backs of them (usually a cluster of at least half a dozen). Which is why dyshidrotic eczema doesn't seem quite right. But I'm not sure they're right for DH either.
Mine break eventually if I scratch them enough, then leave little craters or circles of dry skin. Which also itch like hell 😂 I have to use my teeth to scratch them to get any relief 🤣
Skin stuff is weird.