That's a tragedy, frankly - you have my sympathy. I presume that allergy also covers cats, dogs, sheep, horses, giraffes and other common pets but have you considered a hippo?
Or maybe not I guess
With the best will in the world I can't see lizards and reptiles as cuddly pets either...
I know!! A dolphin (or maybe better get two or three - they are social creatures). Ok you'll need a bigger bath* but don't let that stop you ...
*MUCH bigger