Hi, I'd like to help you with your question.
Most couples fight. Fighting is a healthy way of working out your issues, but only if you disagree fairly and can come to an agreement when it's over. But it sounds like the fighting between you and your girlfriend has become about control and insecurities.
It sounds like there is a power struggle going on in your relationship. Your girlfriend snaps at you, you fight back. Apologies have become very important rather than being close with each other. The inequities have become primary rather than the focus on the two of you as a couple.
Your original ideas of blowing off steam were good. But I am wondering why you both are so angry? Are there unresolved issues from the past such as abusive childhoods? Or are the issues related to something that happened in your relationship, like cheating or lying?
Whatever the issues, they need resolved. Therapy can help you both figure out what is keeping you apart and help you both grow closer. To find a therapist, talk to your doctor about a referral. Or search on line at http://therapists.psychologytoday.com/rms/.
You can also try working on this at home. Here are some resources to help you:
When Anger Hurts Your Relationship: 10 Simple Solutions for Couples Who Fight by Matthew McKay Ph.D.
The Seven Principles for Making Marriage Work: A Practical Guide from the Country's Foremost Relationship Expert by John M. Gottman and Nan Silver
Also, try these ideas when you fight-
Start your statements with "I". This means no yelling "you did this to me". Say instead "I feel hurt because..."
Give each other time to explain how you feel- for example assign 2 minutes to each person. Let that person talk and say how they feel. No interrupting. Then the other person has a turn.
Write out how you feel rather than fight- share your notes and then talk about them.
Include your feelings when you argue- use words like hurt, sad, lonely, etc This helps you get in touch with feelings other than anger.
The better you learn to communicate, the easier it will be to connect when you argue rather than feel apart.
I hope this has helped you,