You need to learn to accept her hair how it is, I think. Frizz never hurt anyone.
If she is being bullied, you need to address that, not bow to the bullying and allow your daughter to modify her appearance to the point where it is impractical for everyday school life - and if swimming is part of everyday school life, you are stuck with it and so is she.]
Allowing her to sit out because she wants to wear contacts and gelled hair is encouraging and whining, pandered to, prinking princess "oh not me, I might break a nail" attitude.
If it doesn't hurt, she should do it. Frizzy hair doesn't hurt, and wearing glasses doesn't hurt.
By allowing her to sit out, you are saying to her "Yes, the bullies are right, your appearance is so unacceptable without gel and contacts that we must do all we can to make sure you keep them". You are teaching her that she is unacceptable as she is.