How can I believe her when there is no affection?

I am a 16 year old guy and I am madly in love with my gf. My gf and I have been dating for a little more than a year now and lately she has not been affectionate at all. For example I went 4 months without her allowing me to kiss her. She plays lacrosse and swims and she is very busy as am I. But in school she won't let me even hold her hand or give her a kiss goodbye. She does not like PDA which I understand but even when we are alone outside of school it seems as if she doesn't want me near her. I bought her tickets to see her favorite artist a few months ago and sometimes feel as if she is only dating me to go to the concert. I need some advice to get her to be more affectionate with me. Everything I tried has failed. She says that she loves me and I know I love her more. But how am I suppose to believe her when I get rejected all the time?