I have a senior lab (13.5 years) who is in pretty good health given his age. Lately when I've been sick and I cough, he gets up and leaves the room. If he's laying in his bed or is actually IN bed with me, he will just leave the room the first time I either cough or sneeze.

What is going on here?

Perhaps he's just trying to watch TV, and is a little tough with all the noise.
Or do you think he is sensing something?
Maybe he doesn't want to catch your cold, at 13.5, he's been down that road before.

The cough, being a jerky reaction could be making him think YOU are going to get up, or you want him out of the bed. Could be the sound or the disturbence. Senior dogs get particular in their old ways. I don't think it's anything to be concerned with, just a funny quirk.

He could have become very sound sensitive. It happens to older pets and things that never bothered them before, bother them now.