How to help a cough if you have high blood pressure?

So my mom has this cough and she’s tried tons of medicines but don’t seem to work. She recently bought that Mucinex DM or whatever and that didnt help either. Any suggestions? Also, my mom has high blood pressure so if you suggest any medicines it has to be a medicine that high blood pressure people can take. Thanks.
I forgot to add, the medication is what starts my moms coughing.