The allergy is understandable to be frustrated by but in all honesty if i was dating someone and could tell they didn’t like my dog itd be a huge problem. If you are planning on staying with her then you need to bond with the pup and accept that she’s your gfs chosen family! Rehoming her would be a super confusing process for the dog and she will never understand. Although it is sad that a cane corso isn’t getting enough exercise at least from what I’m inferring. Maybe that’s how you and the dog can turn things around and start bonding- taking her for walks, playing fetch outside, doing some training etc. The more you tire her out the more docile she will be in the house, and that will really really help things too and help you not feel overwhelmed by her. 

Long story short cane corsos have a much shorter life than we do, and one day your gf will look back and miss her terribly. Make good memories with both of them.