That is tough .. I have two girls who are involved in sports so I can I understand why this would be dificus for you.
I wonder how big your publicense school is... is it large enough you can make other friends? Besides those friends that you had difficulty with?
The other thing is if you play sports ... yout almost make natural friends wig your teammates. Also kids your age do change alot. maybe some of these girls will change..
The other thing is ...is there other sports you are interested in within the private school maybe you could find a new sport to try.
I think you need to work out which is more important to you and if you can potentially make new friends if you go to the public school.