Is cough along with mucus related to wax removal procedure?

Question: Yesterday while on elliptical I noticed my lung capacity was slightly impacted, afterward a cough started accompanied by mucus in throat. Not in my nose (yet). No fever. Last November I got a cold like this that became bronchitis and very stuffed nose that doctor said was bacterial. He gave me an antibiotic for the sinusitis and within a few days I felt much better. The cough lingered for about two weeks afterward. I don't want this to happen again since I'm supposed to leave on a vacation in Quebec on Thursday. I have no idea whether there is any connection to the following: yesterday a nurse practitioner spent an hour trying to dislodge wax in one of my ears. Lots of running warm water in there which didn't work. Any possible connection or am I paranoid? What if anything can I do and what can I take to hasten getting over this?