What do I do, how do I cope, if the person that I'm in love with tells me that looking at me brings back all the pain and hurt we have caused? I'm desperate not to lose them!
It sounds like either you or your partner (or both of you) left a relationship to pursue your new romance. If so, you almost certainly did cause a tremendous amount of pain and hurt. Brain scans show that in recently dumped people, several regions light up -- those associated with love but also pain centers. It's also possible that you two were in a committed relationship and that one (or both) of you betrayed each others' trust through reckless behavior (sexual, gambling, addiction, financial, etc).
It seems to me that there are only a few things you can do.
1) Encourage your new partner to go to individual counseling. Few of us are as responsible and ethical as we wish we could be. Your partner may need to process through the events that led to this realization -- not only that they are capable of harming others, but also that sometimes the only way to move forward is to cause other people pain.
2) You could back off. You could say "look partner, I love you and I want to be with you. But I can understand that you are struggling with recent events, and if it is causing you pain to look at me, then I have to give you space. I would like to hear from you again when and if you are ready to move forward."
3) You could try to talk through the pain with your partner. Maybe s/he needs to be able to verbalize all of his/her emotions and feelings to you. Listening -- really listening -- might allow your partner to reach some closure.