My dog was prescribed diphenoxylate hydrochloride and atropine sulfate oral solution up for a cough?

Hi, your vet is using it "off label" (for a different use than it's generally given) and this is quite normal. The main ingredient is a type of weak opioid, these can be used for controlling coughs as well as for pain and controlling diarrhoea.
I realise this answer will be too late, but for anyone else seeking the same information I would say give it a couple of days and ask for something else if it hasn't worked by then, as it's not very strong at regular doses. It may well do the trick though, the vet has given something that may work fine, you've not been given something unsuitable.