Maybe get some suggestions from a pharmacist or GP on possible soap for your skin.

Moo Goo and Dove are good on my skin.

I can never used anything highly perfumed but in saying that I find good old Imperial Leather really nice. It leaves your skin soft

My husband has sensitive skin and finds that Graham’s Natural Body Wash works for him. He buys it online. He also uses Redwin’s Body Wash and finds it works well too.

Moogoo is great

Have you tried products of the freshwater farm ? I think they’re amazing and feed the skin instead of stripping it
https://freshwaterfarm.com.au/collections/shop-all

I use Aveeno – the blue one, called skin relief moisturising body wash.
I get rashes and break out in hives using all other ones, which is really such a shame as my skin was never like this before pregnancy!