I definitely had problems like this when I was first diagnosed and when glutened now - even if it was only a small amount. It was AWFUL! I mountaineer, so I went from 20+ mile and crazy elevation gain hiking/climbing trips to barely being able to move around my apartment. Do you have edema? Bad edema days make me feel weighty and sluggish (and I am weighty with edema - I lost 15lbs of water weight within 4 days of going gluten free - seriously not kidding!). Stick to the diet, especially if your IgG level is super elevated. I had a positive biopsy but my only positive blood test was the IgG which was 4x higher than the normal level. IgG's are not specific, meaning they can bind to other similar proteins in addition to gluten. I started out on the SCD diet when I was first diagnosed because I was reacting to all grains and some other proteins that are supposedly similar to gluten, but now that my antibody levels are normalizing I've been able to start eating more. Sorry that was a bit rambly - it's getting late over here!
Are you sure they were hives? Did they show up immediately or fairly soon after? It definitely sounds like an allergy, but I've had problems where i touch gluten and get a dry itch rash ~2 hours later. ick. I really hope you figure it out!
Some of us are more sensitive than the 10 or 20 ppm limit they put on gluten free foods. I have only a small handful (literally small, maybe 3-5?) processed products I can tolerate. It's also possible that you have other intolerances. Have you tried giving up dairy? soy? fructose?
I know for me there was a "grace period", where cutting out gluten as an ingredient in anything but still using the same pots and pans (though thoroughly cleaned) was totally ok for me, and definitely helped me get a handle on things without an added pressing stress. After a while gluten-free, my sensitivity and my reaction got stronger, so I definitely had to buy all new pots and pans. I tried scrubbing them and bleaching them (since it denatures proteins, not sure if it works on gluten but it made me feel better), but still found that many of them bothered me. Definitely replace scratched non-stick pans, cutting boards, and wooden utensils and boards. I found I was ok with unscratched glass though - after scrubbing multiple times and bleaching. In general, I tend to be more sensitive than most I think.