Does loving someone means letting them go?

I am a bi and have a girlfriend that recently just broke up with me..She's a bUtch(not *****) and she has been with me for a few months now,though things didnt really end things with her ex I decided to start a relationship with her because she said she didnt love her girlfriend anymore and has no feelings for her whatsoever.However,recently things start to change and they got intimate and now my girlfriend tells me she found out she still has feelings for her ex.It kinda feels she cheated on me and that I was with her just to fill her loneliness but I couldnt let her go because I love her so much and to me it didnt matter.Now,I have a hard time letting her go.Should I text her about this whole situation?(Its really hard because she seldom replies me already) Or should I just let her go?I want to but it just seems so hard especially when I see her together with her ex.I just feel crushed and devastated.I want her to be happy but at the expense of my happiness?Do I really have to let her go back to her ex if I love her?My heart cant let it go though I want her so much to be mine.What should I do?