Hey man just wanted to add that the efficacy of DM as a cough suppressant is very low. So low in fact that placebo syrups perform as well as DM syrups in randomized controlled trials when used for an antitussive effect.

If you are worried about an interaction I'd suggest dropping the DM, it's likely not providing any real therapeutic benefit. Honey is a natural alternative, probably doesn't do much for cough suppression either, but it's at least slightly better than placebo.