I like someone but my ego stops me from liking them?

so there's this girl in all my classes who I'm very competitive with. Eventually I decided I liked her, but for some reason I find it very hard to be nice to her and express that I like her

I think it's because she's a very egotistical person so showing her attention is just quite hard

Should I try and get over my ego or is she just the wrong type of person to like? If I actually like her then why does it feel like such a power struggle between us