Given all that you have said, esp. the fact that things are fine between you now, my answer is no. Going back to her now to add something like, “I know I said bad things about you” will likely underline the good relationship you have now.

Let me say it this way. If she doesn’t have a problem, then why add to her burdens? Why confess something when forgiveness has evidently already been offered? Why cause her possible anguish over what you may have said?

It’s possible to have an overly-scrupulous conscience. In that case you would do well to talk this out with a friend who is not directly connected and ask that friend to pray with you and for you that you can let go of your own sins.

On a few occasions I have had well-meaning people come and apologize for saying unkind things about me behind my back. These were people I had no idea were talking about me. I never felt good about that. I suppose their confession was good for their soul, but since I knew nothing about it, it did me no good. A person in that situation starts thinking, “I wonder what they were saying.” Listening to them felt more like therapy for them than anything that would be helpful to me. Note that in the case I’m describing . . .

I didn’t know they had said anything negative about me.
I didn’t consider the relationship broken.
I had no way of knowing the details.

What’s the point of the confession in that situation? To make them feel better, I suppose.

In your case you confessed your part in the broken relationship and evidently were forgiven. You did well to make things right. But that should close the book on the past. Unless your friend brings it up, I see no reason to go back to her with yet another confession.

See Is Total Forgiveness Realistic?