If you and your girlfriend were in love at one time but then broke up and had some bad fights is it possible to get back with each other later on?

Not unless you are both willing to learn how to communicate and mature. It would be best if you gave each other head space to figure out who and what you are in yourselves and what you want out of life. This also makes one mature on a more rapid basis. Yes, it's possible you could get back together again, but make the separation worth it and each of you has to learn to give and communicate if you want any relationship to work well.