Hi, I'd like to help you with your question.
If you both feel strongly about each other, then you should stay together. But in order to do so, you need to work out the commitment issue. As long as you have the problem that broke you up still there, you cannot move forward.
A good test of your relationship and it's future would be to start working out the commitment problem. Staying committed to each other from a long distance is not easy. So finding ways to address this issue is primary. Also, you may want to consider working on a way you can eventually be together. Being apart is very stressful on a relationship and in order to know if you both can be together permanently as a couple, the distance part of your relationship needs resolved.
Here are some resources to help you. You can use them apart then come together to talk about them:
The Long-Distance Relationship Survival Guide by XXXXX XXXXX and Kate Brauer-Bell
The Long Distance Relationship Guidebook by Sylvia Shipp
He's Scared, She's Scared: Understanding the Hidden Fears That Sabotage Your Relationships by XXXXX XXXXX and Julia Sokol
Getting to Commitment: Overcoming the 8 Greatest Obstacles to Lasting Connection (And Finding the Courage to Love) by XXXXX XXXXX and Julia Sokol
You can find these books on Amazon.com or your local library may have them for you.
There is nothing wrong with trying again. You and your boyfriend have tried separate ways and feel that being together makes you happiest. It is worth a try.
I hope this has helped you,