What should you do when you hurt a loved one unintentionally resulting in a break-up but deep down you still love each other?

I had been going out with this amazing girl for 4 & a half years, I loved her so much, but Never fully showed her how much I appreciated her, I didn�t get involved with her family and friends because of a (drug related) social phobia which I got over but kept thinking it was too late to do anything about. We recently broke up because I wanted to ask for her to marry me, but Wanted some time to see if It was right and my feelings where true I thought if she takes me back and I want to go back then I�ll have my answer. I broke up with her and realised how much I loved her and was so happy when we agreed to get back together & that I would get the opportunity to propose. Then She found some messages on my phone from another girl who I had kept secret! And lied about. It was never a relationship nothing physical or emotional ever happened I was just to scare to tell her about this person for fear she might leave me. Which She did & I�m still madly in love with her but she doesn�t feel the same, but she still is giving up hope on the future because we are still speaking & I can tell she has feelings for me she has told me & I can see it in her eyes feel it in her hugs & body langue, I cant understand because we were so great together and I believe in my hart that she still loves me and I cant give up hope and will wait and fight for her love (but not forever) because I honestly believe she is the one and up until 2months ago she was saying the same thing, Its very painful but I feel I have something to prove so IM getting on with my life and perusing my individual goals but still keeping hope that one day we will be together. What I want to do is prove to her I have changed in a lot of positive ways, all the things that weren�t in our relationship before I want to introduce, and I�ve never cheated on her and could never do it, because she means too much to me, to hurt and I hate my self for hurting her but I want to prove myself but not come across to strongly. I�m finding it hard to deal with only contact once a weak and the possibility of her finding some one else (even though she said she is not looking) who is better than me, before I get the chance to show her how Good I can be, My drive is to make myself a better person & to make her happy I love making her happy her smile give me such a high, How can I deal with waiting and stopping my self from �pushing.� Because everything she loved about me is still here, and everything she wasn�t happy with I can feel within myself has changed. I don�t mind getting trying and failing to win her back but, failing without trying is something I Just can�t do!!!! I had been going out with this amazing girl for 4 & a half years, I loved her so much, but Never fully showed her how much I appreciated her, I didn�t get involved with her family and friends because of a (drug related) social phobia which I got over but kept thinking it was too late to do anything about. We recently broke up because I wanted to ask for her to marry me, but Wanted some time to see if It was right and my feelings where true I thought if she takes me back and I want to go back then I�ll have my answer. I broke up with her and realised how much I loved her and was so happy when we agreed to get back together & that I would get the opportunity to propose. Then She found some messages on my phone from another girl who I had kept secret! And lied about. It was never a relationship nothing physical or emotional ever happened I was just to scare to tell her about this person for fear she might leave me. Which She did & I�m still madly in love with her but she doesn�t feel the same, but she still is giving up hope on the future because we are still speaking & I can tell she has feelings for me she has told me & I can see it in her eyes feel it in her hugs & body langue, I cant understand because we were so great together and I believe in my hart that she still loves me and I cant give up hope and will wait and fight for her love (but not forever) because I honestly believe she is the one and up until 2months ago she was saying the same thing, Its very painful but I feel I have something to prove so IM getting on with my life and perusing my individual goals but still keeping hope that one day we will be together. What I want to do is prove to her I have changed in a lot of positive ways, all the things that weren�t in our relationship before I want to introduce, and I�ve never cheated on her and could never do it, because she means too much to me, to hurt and I hate my self for hurting her but I want to prove myself but not come across to strongly. I�m finding it hard to deal with only contact once a weak and the possibility of her finding some one else (even though she said she is not looking) who is better than me, before I get the chance to show her how Good I can be, My drive is to make myself a better person & to make her happy I love making her happy her smile give me such a high, How can I deal with waiting and stopping my self from �pushing.� Because everything she loved about me is still here, and everything she wasn�t happy with I can feel within myself has changed. I don�t mind getting trying and failing to win her back but, failing without trying is something I Just can�t do!!!!