What should I rinse my mouth with?

So I have had bleeding gums which have been slightly inflamed. Flossing would just make them bleed and hurt afterwards. I just recently got my cleaning & my dentist told me to get listerine mouth wash. I bought the clinical solutions one. I have noticed that the bleeding has reduced significantly & my gums are less inflamed.

But I am super confused on what to do because I see people saying mouthwash with alcohol is bad for you & don't use it. So will this harm my teeth in the long run? Why is it helping my teeth if it's "a waste of time"? And what could I replace it with if need be?

I don't really wanna throw a whole bottle of mouthwash away.