My friend and I had an argument a few months ago. It was a really bad one, and we both screamed and yelled at each other. I stopped talking to her after that, and since then, she has gone to each of our mutual friends and told them about our fight. I haven't done that. In fact, I haven't mentioned it to anyone else.
But the thing is, our friends are treating me differently. I still haven't said anything to them, but now I wonder if I should?
Taking the high road isn't easy, especially when other people attack or tell "their side" of your argument. Your friend is trying to get people on her side because she's probably hurting after your argument. She thinks that getting people to agree with her version of things or even to tell her that you were the one who was wrong will make her feel better.
And in fact, it will. For a short time. That's why people do it.
Remember the Big Picture and Be Respectful of Your Friendship
You seem to have a grasp on the bigger picture, which is that when you run to other people and tell them about something that should be kept between two friends, it makes you look bad. Even if people agree with you and tell you what you desperately want to hear, it gives others the impression that you're someone who will spill secrets of a friendship to anyone who wants to listen.
Bottom line, if you try and get people on your side, they'll remember that you did that, and eventually when they have a problem with you, it will make them less willing to be honest and work things out. They might even avoid conflict with you out of fear that you'll trash their name to your mutual friends.
Still, as you mentioned, it's hard to take the high road when someone is talking about you to friends. It's even more difficult when those friends seem to turn their backs or look at you differently.
Stay the Distance in Order to Reap the Benefits of the High Road
However, there comes a point when the high road becomes easier, and if you can hold out that long, it feels so much better than if you had stooped to your friend's level and talked about your argument to other people.
Your friends may be treating you differently now, but give it some time. If they actually stop talking to you, then approach them and ask them why. (Don't assume it's because of this recent argument with your other friend.)
If one of these friends asks you about this argument, tell them the truth but don't dramatize it or be disrespectful to your friend. Set the record straight if you have to, but then move the conversation along so that you are not talking behind your friend's back (like she did to you.)
How to Set the Record Straight and Still Be Respectful of Your Friendship
If another friend asks about the fight, you might want to say:
"Yes, Susie and I had an argument, and I'm very disappointed that she felt the need to share that with you. I feel like I'd be doing her and our friendship an injustice if I talked about the details, though. I want to be as respectful as I can."
Friend: "Susie told me you just blocked her on Facebook for no reason. What's going on?"
You: "I did block her. It was after our argument and there were several significant things that were said and never resolved. I'd prefer not to talk about it out of respect for our friendship."
Incidentally, you can say "out of respect for our friendship" even if you have decided to move on from the relationship. There's no reason to talk badly about your friend even after you end the friendship.
If a friend asks about something specific, you might have to clear the air, however. For instance:
Friend: "I can't believe you got mad at Susie for going to the concert without you. Don't you think you're overreacting?"
You: "That's not what happened at all. Either you heard that wrong or Susie is not being truthful. I'd prefer not talk about it because I feel like it's disrespectful to our friendship."
If you're pushed, clear the facts but don't badmouth your friend.
"That's not what happened. Susie has blown me off for events several times before. I was tired of being used that way. This isn't an isolated event. However, I am sad about what happened."
It's unrealistic to believe you'll never have to talk about your argument at least in part, but do your best to be respectful and if you feel yourself wanting to unload so you can "tell your side," take a mental step back and use caution with the words you say. Stay as close to the high road as you can because it will be better for you and all your friendships (even the one you had to end) in the long run.