Just in case this isn’t a bit: OP, the structure in English should be “adjective noun.” The opposite to most romantic languages where you say the noun then the description word. So a cat girl is a girl (assumed human) that can be described as a cat (has the traits of a cat). A girl cat is more reasonably a cat that is a girl, though you’d probably say “female cat” more often. For allergies you’d want to look into hypoallergenic cats like the hairless sphynx.

It’s really got the same vibe as constantly comparing someone to your ex.