Other than something like Decent Exposures as already mentioned, or perhaps Molke, which is again a cotton non-wired bra, I don't know of anything. maybe the British brand Royce might have something, as they make exclusively wire-free bras in conventional bra sizing. But they aren't necessarily hypo-allergenic.

I fear, though, that as a Deco girl you'll be sadly disappointed by Decent Exposures or Molke for a daily wearer. They would be great as leisure bras and great to help you heal up, or if this is really a contact dermatitis, then maybe once you heal up you could find something different for going out (maybe with a liner)and have a cotton bra for at-home wear.

But, not to contradict your doctor and i'm maybe on thin ice here because medical advice is not allowed on the sub. But, well, it's easy for your doctor to say "get a hypoallergenic bra" when there's not a lot on the market that qualifies as such, and what there is , si going to give a vastly different look under clothing than what you're accustomed to.

Now, if it turns out that it's what you need to do, it's what you need to do. But I'm just wondering if there could be a fit issue here that's caused the rash. Where is it on your breasts, if you're comfortable saying? Is it possible that your wires aren't sitting in your IMF and you're getting skin-on-skin contact?