I think you are being too hard on yourself.
OK, maybe you were a little hot-headed, but people make mistakes - that's why they put rubbers on the end of pencils!
I think you should do two things - stop beating yourself up over a row, which takes two, and which you have not provoked, and let time take its course, and keep talking.
As Cina suggests, some Relationship counselling may well help you both to explore your feelings and move forward from this.
Hope things work out - please let us know.