I went in with a cough, but the anesthesiologist listened to my chest and found me clear enough for surgery. It was the end of a cough and I could sleep and breath well, so I figured I'd be fine.
But when I came out of surgery, having to cough proved to be a HUGE problem for me. Oh the pain! They told me to "splint" my belly with a pillow when I had to cough to minimize the pain, and though it helped some, it didn't help much. I found myself sitting there for several minutes at a time, my husband holding my hand, just trying to get one cough out. I couldn't do it because I knew how it felt. Now, the docs will encourage you to cough after surgery so you can clear your lungs of any gunk that settled while you were out (to avoid lung infection), but personally the less coughing I could do the better; so the cough I really wish I could've let fade before going in.
Sneezing...holy cow. I'm allergic to just about everything, so I was surprised to find that I didn't need to sneeze. I've literally sneezed twice since my surgery, but they were not pretty. OUCH! Since then, though my port site seems to have healed, I've avoided sneezing at all costs because even the memory of the pain keeps me from getting it out. Kind of like negative reinforcement for a pet or child...haha.
Anyway, this isn't meant to scare you, just sharing my experience. I found myself saying that I should've let the cough go away; and it seemed my port site took a tad longer to heal than others, maybe because of the coughing and how my ab muscle was involved in having to do so. But as mentioned above, definitely tell the docs about it. They told me as long as I didn't have a fever and my lungs sound clear I should be fine, but you're obviously not me. =D
Good luck!