Should I have gone back to apologize?

Today I got in a fight with an authority figure where I said some pretty mean and arrogant things. A friend was there with me, and on the drive home I told her how bad I felt about it. She suggested I immediately go back to apologize, but I didn’t think that was the best decision, what with both of us still being pretty upset. Instead I decided to go straight home and e-mail my apology. What do you think would have been the best decision? In the future, is it better to make an immediate personal apology while tempers are still high, or to wait for everyone to calm down?