I have to take the opposing view. Since you got it from a public website, you didn't create or purchase it, you don't own it. So it was perfectly all right for her or anyone (or everyone) else to use it, too.
It's nice to have an avatar that's uniquely yours. People have only to glance at it and they'll know you're the one posting.
But IMO, it's not a critical thing. I see nothing wrong with several people using the same avatar. Some message boards provide a set of avatars for people to choose from, so you see a lot of people with the same one. In those cases, it's not a unique identifier, but it still tells everyone something about that person's personality.
It's like women getting upset because someone else at the same party is wearing the same dress. Hey, if you got it off the rack, you have to expect that to happen.
You handled it graciously, asking her first, then accepting it (however unwillingly) and changing your picture. The new one is very sweet, but honestly, if you loved the old one, I see nothing wrong with using it just because someone else uses it, too.