Hi p3 and welcome to the forum.
I get allergy shots weekly. It takes several months of building up the doses for the shots to work. This year I developped a new allergy to grass and have been building up doses for that since early spring - not finished yet! But the doc is right about calling it quits after a whole year.
It's possible you are allergic to something he's not tested for. Rash is something I don't get with my inhalation allergies - pollen, dust, mites. A bunch of the meds you are taking could be part of the problem too. I am sensitive (official term, but my allergist says it's an allergy too) to coloring agents, sweeteners, and things like gelatin which are found in lots of meds, especially the liquid ones. I'd drop anything not prescribed. And I certainly wouldn't add anything over the counter, especially herbals until the shots have had a few months to build up.
You could have contact rash from detergents, fabric softeners, shampoos, soaps, skin creams, and that list can be huge. I only use All Free-and-Clear, double rinse, and no fabric softener. I will throw in a free-and-clear dryer sheet if I'm drying something that will have a lot of static. Towels dry you better without fabric softener anyway!
Then there's foods! Have you been skin tested for them? And skin testing won't catch nearly all of them!!!!! I had to give up anything processed - nothing I don't cook myself from scratch, and even then no onions or garlic or pepper or gelatin or corn starch. Nothing that has any processing. But that's my allergies. My allergist had me keep a food diary/log/journal, with my reactions, times, etc. For migraine people foods can cause a reaction 2 days later.