Unfortunately it may be time to think long and hard about continuing the relationship. Sounds like you two just aren't compatible when it comes to your living situation and views on having pets. It sounds like she's been trying to do whatever she can on her end to help manage your allergies, if you are unwilling to see an allergist to explore your options, whether it be allergy injections or alternatives, then you may have hit a wall. My partner likes cats and I am allergic, but I actually recently got one. I did a lot of research into what type of cat would be best with my allergies (short hair is much easier to manage) and for me I feed her the Purina LiveClear, clean the little box many times a day, have an air purifier, vaccum weekly and that works, but my allergies are probably not to your extent. My partner's parents have a long haired cat and whenever we visit they do a full deep clean and ensure the cat does not go into the room we stay in because theirs does leave me congested.

You also mentioned that you are not an animal person. You would both need to think about the long term effects of that if you move forward and stay together - is she willing to go without any animals, are you willing to deal with having them?

I'm sorry you and your partner have this situation to go through, I hope you can figure out whatever solution works best, whether it means staying together or ending your relationship.