Quoted from jgentry:
Depending on your girlfriends allergy no amount of pills or air filters may allow her to live a decent quality of life with them.
I also love cats, but am extremely allergic.
I took twice weekly allergy shots for over a decade. This allowed me to exist in the same house with them, but I could by no means pet them or otherwise do anything that involved being near them for any length of time. This was a giant time commitment (for the shots) and was much more than a stuffy nose (in severity). When I was 17, I stopped taking shots, and now I am so allergic that my throat closes off and I cannot breathe when I am exposed to them for more than a day or so. I immediately start itching and break out in hives when I am near them, so I have that going for me. Going to others' houses with cats is always a challenge, or working on a game filled with cat hair. I make the best of it, but it is quite scary to be unable to breathe when there is nothing that should be preventing it.
And I don't think I have the most extreme cat allergy on the planet, either. So it can be quite serious.
While mild allergies might go away with time, and perhaps my continual exposure to the allergen (then complete lack thereof) in the form of shots is to blame for my new extreme allergy, this is not going to be the case for everyone with allergies.
I would not mind having another cat, but I do choose to continue living (for now), so no cats in my immediate future. Good luck rehoming your cats, OP.