Woah! Don't give up on her yet! If you could walk away from your relationship with her, and never question whether that decision was right or wrong... then maybe walking away is the right thing to do. However, if you feel that walking away would cause you to doubt your decision, then in my opinion it's not over.
Obviously she is insecure. Help her. Make her feel good. (the dress) - You were walking out the door - but was what you had to do so completely important that you couldn't see her first!? I could see if it was truly important, maybe an emergency, but c'mon...you guys had been fighting for a while. In her mind this may have been a chance for you guys to see eachother and make things better. She may have been really excited to see you and looking for the mutual excitement. I myself would be upset if I didn't get the same in return. I think she likes you a lot more than you think. Her feelings for you are obviously strong if she is getting jealous over M. Maybe you need to have a talk about how you both (((really))) feel about eachother.
J and I sound a lot alike. I am in love with somebody that I pushed away. I did the same thing to him. Unfortunately it's too late for us. I assumed the worst all the time. I assumed he didn't care through the smallest things. Consider the small things that she gets angry over. Could you prevent some of those things in the future? Is it worth it to you?
One of the best things you two can do (especially you) is watch how you speak to eachother. Watch your tones. If you "hurt" her feelings, let her know that you didn't mean to. Ask what you can do to make it better.
It sounds like I am taking her side.... this is not true. Like I mentioned, I lost the one I cared about because I pushed him away in the exact same way. You have to let her know that you cannot read her mind. If the communication is not clear, then there will be no improvement. You can only take so much huh. Maybe through your time apart she will realize that at times she could have explained herself better, or she could have not overreacted so badly. (If you haven't taken time apart.....you should do that!!!!!) I bet time away from you will make her realize how much more she likes to be with you and your little imperfections as opposed to not being with you at all.
Hope this helps.