I have gum disease and as part of my daily regime I use a water irrigation tool to help clean out my gums. I use a Waterpik with the regular pik and the pik pocket pik to clean out my gums (I have tooth pockets ranging from 1 mm to 7 mm). I start with that (I usually put hydrogen peroxide - to whiten teeth and kill bacteria, a gum mouth wash for gum disease, and an anti-biofilm mouth wash for my teeth in with warm water), then use traditional floss to get everything else out (sometimes I dip the floss in the anti-biofilm mouth wash to get it in my gums), followed by traditional brushing, and I then rinse my mouth out with a mouth wash that has fluoride, xyitol, and lemon peel oil.
But I have to do this because I had bleeding gums, big teeth pockets, loose gums, tartar build up, etc. Not just because I had red gums.
Talk to your dentist about what your daily regime should look like - I'm assuming your dentist wants you to do more than just brush and use a mouth wash. Talk about how you should be flossing and how to floss (water irrigation or traditional flossing or both), what foods to avoid in your diet, etc.
As for the mouth washes, I don't use any prescription ones, just ones that are geared towards my symptoms and come highly recommend.
Btw- in case you're wondering what mouth washes I use: Biotene Oral Rinse, Therabreath Icy Mint Oral Rinse, and Therabreath Peridotherapy Oral Rinse.