I discovered I’m allergic to dogs after getting my first dog as an adult - although only mildly. I was already in love with him from the time we chose him so no way was I going to do without him. I just take steps to manage it.
I understand that a more severe allergy is harder to deal with. However, it does sound like your dog is only one cause of her allergic reaction. So I think it’s a bit soon to jump to rehoming your dog.
There are definitely things to try first to see what makes a difference.
— first, you could get a cleaning company in to do a real professional deep clean - get rid of all dust/dog dander/etc in your home
and get your dog groomed professionally too
Then you’d be starting from scratch with a fresh environment. from there:
— restrict the areas your dog goes in - that would be hard enough for both you and your dog and a huge compromise in itself
— wash the dog’s bedding regularly
— consider getting a regular cleaner - you will be sharing bills you’ve paying yourself up to now. So use some of the extra for professional cleaning, paying close attention to areas your dog is in most
— if your GF works from home then could you put your dog to a doggy daycare so he’s not home all day or could family or friends help out and have him at their house during the day
and then if your GF also tried some allergy remedies, all of that combined could make this totally manageable.
I definitely wouldn’t rehome til you’ve tried at least some of that. And if she isn’t willing to even try so that you don’t have to give up a pet that you love and are bonded to, then that’s honestly a big red flag