Can you trust her? Sure, if you want. Trust comes from you, not her.
You are confusing trust with 'trustworthy'. Your question should be: is she trustworthy? No, I wouldn't say so.
Are there things she can or should be doing to increase her trustworthiness? I would say yes, but she doesn't seem to care enough to want to. That should give you your answer. At your age, it really isn't worth it to drag your own heart through the muck with girls like this. Move on is my advice.
Second thoughts can generally be amended with judicious action; injudicious actions can seldom be recovered with second thoughts.
--Cyteen by C.J.Cherryh