dude. STOP STOP STOP STOP STOP!
your are right in the fact that you need to move on...you need to get away from her, no matter what you did at this point you are broken up she has no right to still be upset with you...this "new bf" is a rebound and rebound relationships DO NOT LAST, period, its that simple...shes dating him to get over you...
girls are crazy man, they say one thing, but really don't mean it, they say it to see how you react to it...i know you love her and care about her but right now you need to do what makes you happy...be there for her when she needs you but only when she NEEDS you...you aren't going to be this guy to fall to her every single need ok...like I said be there for her to talk to and help her through some troubles...but you need to remember right now youa re her FRIEND, not her bf...by being there for her and being a NICE guy - that's key you have to be nice no matter what she says - this will show her that she's a btch for no reason - kill her with kindness...got it!?
i went through this sitaution and I begged for my ex back...she dated a dude for 6 months, I didn't interfear but I was there to LISTEN to her when she would get in fights with him...did I give my two sense of course I did...i always asked, why do you like him, what do you like about him, why are you dating him...i knew he was a rebound and he in fact was...now she wants to get back together with me, but I dont...i need to build our trust back - because that's the key to the success of a relationship...remember to take things SLOW and STEADY - it was the turtle who won the race, NOT the rabbit...
now is your time to analyze the relationship, what went wrong, was it all your fault (most likely not - a relationship ends because of multiple things), but analyze teh relationship, understand where YOU went wrong and work on yourself to become a better person, more mature...show her and others through your actions that you area better guy and more relaxed, but only do it if you are, no need to be fake, feel me?
really work on yourself and being independat at this time...if she yells at you for no reason just reply with a simple "k"...girls HATE that, they want to see you explode, they want to see how you are going to react to what they are saying to you (especially ex girlfriends)...by saying "k" you are letting her mind tick...ex) wtf k, what does that mean, does he care, why isn't he respondign with more, omg am I losing him, what is he doing, etc etc...you need to ler her think about what your doing and WHY you are doing it...dont update her with stuff that your doing, when she talks to you be short adn simple about it...you want her to feel that she's losing you, losing a good guy, losing something that you could ahve worked out...but this is also for you to help get over her faster...keeping communication to a minimum is key for you, not only getting her back but really its also for you to heal...time wil heal my man, take my word for it