I think you should, that's dangerous to not treat a torn fin like that. The closer to the body, the easier it is for fin rot to set in and start eating at the body. So QT her and get her fixed up with some Stress Coat, you can use .5 teaspoon of AQ salt (dissolved first) as a preventative measure for 5-7 days. Change her water every day, add the salt in and use the double dose of Stress Coat and it should start healing very soon! But keep her in the QT until it grows back more or less all of it. Use the salt just for up to 7 day's since it's not fin rot yet, just a preventative. Then just water change everyday until she heals.
My bet is on the tetras as well