Breakingheart

I don't know where else to take this and I really need other opinions on this. I can't get therapy for some time so in the meantime here I am. My girlfriend of two years left state for five weeks and I cheated on her while she was gone. She is still gone. She found out. And as of right now she says she wants to fix it and still loves me, but she won't speak to me. She says she needs time and space. When I say she won't speak to me I mean, no contact, nothing. I really made a big mistake and I've contemplated drastic things if I can't repair the mess I've made. Does she still love me ? Is there really any hope? I don't understand the distance thing. Is she just trying to get rid of me without telling me?