I'm not to make amends with a friend who stopped talking with me but wants to reconnect.
Did you ever find out why they stopped talking to you?
Yes, it was because of I told them something they didn't like.
It is fine to not want to have a relationship with a friend that hurts you. If you feel uncomfortable with them, then it is okay to separate. In time, you may come to a different conclusion and you can re-address the situation again.
You know, it's me who has to do something as I made a mistake, not them.
I am glad you want to apologize as cutting someone off isn't necessarily always the best option. I hope everything goes well for both of you!