Your words were that you went against everybody's advice and buckled under the pressure. I think you got a mix of advice, acknowledging that you *did* have a very difficult choice. Sometimes you have to learn what is important to yourself by doing it the "wrong" way first. I know I've learned most of my tough lessons that way. Remember--you can change your mind even if you did make a promise.
You've got options. One is trying to write the letter. I think you know what will come of that.
Here's another option you may not have thought about:Tell your partner something like this:
I ___ed up when I promised to cut contact with my friend, [name]. I thought it would make you happy, so I acted against my own values, and abandoned a dear friend at a time when she needed support.
I still want to make you happy. This is too high a price to pay. I hope you will stay with me even though I cannot do this for you anymore.
Think about it. Those aren't your words, so work out what it would be in your words. Think about whether you want to say something different or offer something different.
Then think about how you would feel about doing this. (And presumably getting back in touch with your friend and apologizing.)
Let me be clear--I'm NOT recommending that you go out and DO this right now. Just think about it and how you would feel, how you would handle your partner's sure-to-be-bad reaction.
You don't have any 'easy' choices in this matter. Anything you do will be difficult. Anything you do runs a good chance of hurting at least one of yourself, your partner, or your friend.
GK