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.
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.