I too have an allergy to a wetsuit allergy - my notes here suggest it was IPBC, but I was discussing this with my dermatologist recently and this sounds more likely to what you have. I was told that it was an additive put into neoprene as a preservative. What originally set me off was a Nineteen Pipeline that I had rented from a local tri shop. But this was many years ago, and I've since found solutions.

I've since bought 2 wetsuits that have served me well:

• Desoto Black Pearl is made from a material that isn't neoprene. Emilio here was very good at helping me through the process, but like everything, he said he couldn't control what happens upstream. I can't speak for him for your situation, but he was willing to refund me a wetsuit if it didn't work. The wetsuit served me well, but after getting into the sport for a few years, I decided to upgrade for a fancy suit with some of the perks that you read about.
• Roka Maverick pro is my current wetsuit, and hasn't given me any issues. I was lucky that a friend had this suit and was willing to lend it to me to test. No reaction.

My advice is to find other swimmers and ask to borrow their wetsuits for spin, or just keep trying wetsuits at various shops. Let them know what you're doing and try on a suit for 20 mins and see what happens. I know it can be hard since each reaction is like a month of recovery (at least for me), but you don't have to wear the suit on your whole body. I tested the Roka on my legs at my desk before I decided to see what would happen if I sweat in it. I've also tried my Dad's Zoot (can't remember the model) and it didn't give any issues either, but I preferred the Roka to swim in.

My understanding is that this is primarily a lower quality / older model issue. You might have better luck (as I did) shopping at the higher end of the wetsuit price range.

I actually don't use the Black Pearl (Size 4) anymore and am willing to part with it on the cheap, though I'm in Canada so might get tricky trying to arrange something.