I think just talking to her and getting things clear will be better. Open conversation as to what makes her think that you are clingy will help the situation. And sometimes we all need boundaries even with our best friends. So if you communicate and ask her what exactly makes her think that you are clingy will be useful so that you can also know if you are making some mistakes.
I think clearing out about what you think about your friendship and you are not being clingy.
Also try tk focus more on yourself than on anyone else.