Need some help! What should I do?

Ok a little over a week ago my gf and I broke up... we were fighting and bickering alot at eachother...But at the same time we both really care for eachother... I'm positive this girl was crazy about me... "Do you want me to make you something to eat, How are you feeling? Do you want me to pick you up Taco Bell...etc" And I could just tell by the way she would stare at me that she loved me. Then we broke up and I was the one that said it out of anger... She has lots of problems and she is always working on them...Ever since I broke up with her I have wanted her back... and she is saying "I need to be alone right now, this is to stressful we can still be cuddle buddies" I have tried my best giving her space and not talking to her much but trust me its hard... My family is throwing a birthday party for me this weekend and I invited her... she said "I'll be there" I'm sure there isnt another guy that she is seeing, and I want to know if there is anyway to repair this and we go out again?