When I was a teenager we had a rescue cat with a severe flea allergy. He was on a strict flea treatment regimen and steroids. Unfortunately he still went outside, but us kids had no control over that.
I have a detergent allergy too. I had a sample of something and made the mistake of washing my sheets in it. I had to rewash them the next day I got such a bad skin reaction from it.
Normally I use Method Free + Clear, maybe you could try that for the kitty's bedding? I use it for my cats' bedding too. I used to use Tide Free, but I started having problems with that too.
I have a detergent allergy too. I had a sample of something and made the mistake of washing my sheets in it. I had to rewash them the next day I got such a bad skin reaction from it.