I’m not Qadgop, but… the over-the-counter cough suppressants supposedly don’t do all that much to actually suppress the cough.
Dextromethorphan - Wikipedia (“However, controlled studies have found the symptomatic effectiveness of dextromethorphan similar to placebo”)
I haven’t found that it does much for me (nor does benzonatate, which is prescription and mentioned in that first link). For a less-severe cough - such as the one caused when I started lisinopril (BP med), codeine did reduce the cough when I took it for a couple nights. I don’t know the mechanism by which it works; in the case of the BP-med side effect it was NOT a respiratory issue at play. When I had that vicious case of bronchitis, it’s hard to tell whether it worked or not but it was worth a try. They actually make cough preparations with even stronger narcotics such as hydrocodone.