Well... from what you wrote... it doesn't sound as though you did anything terrible.
This sounds as though it was pretty innocent to me.
And I think your friend was correct. You were young. My personal opinion is that you can't judge something you may have done at age 13 by the standards you hold today. You didn't mention how your friend reacted to your apology. Hopefully she was gracious in her reply & that the two of you can remain friends.
Here are links to 2 articles, from PsychCentral's archives, on the subject of how to deal with feelings of guilt & forgive yourself. Hopefully some of the information in them can be of some help:
https://psychcentral.com/blog/5-tips...ng-with-guilt/
https://psychcentral.com/lib/how-do-...give-yourself/
I wish you well...