Easy for me to say as I'm not in your shoes but I would take it one step at a time. Instead of turning ourself inside out and changing your preformance style just do what you can till you have to take off. Talk to the management or whomever and I'm sure you know people who can fill in who you TRUST. Trust is the big thing as I just had a bad expierence taking two weeks off from a gig.
Listen to the Docs and don't push yourself and possibly make things worse. You've heard it from everyone, your health is most important. Work is just work, even in music. There are always stories about preformers cancelling shows and even tours for health reasons.
Good Luck

Uncle Dave. Perhaps nothing to worry about but best to get things checked.
Had a similar problem for some time, felt like something at back of my throat that made me keep coughing to clear it, but it would not clear. Saw specialist who put camera up each nostril and down to vocal chords and stated everything was fine, he explained that I had Acid Reflux which drained upwards from my gut overnight and causing throat irritation. Suggested I cut out Coffee,Tea and fizzy drinks...So I'm staying on the whisky !!!.

Jim Beam Honey Bourbon works quite well for me. Gotta restock the liquor cabinet today - supplies are getting low.

Gary

Mostly good points, thanks all ... but Gary - booze is not the answer for me. The scotch cotton balls had a teeny, tiny amount that just numbed the area. I rarely use alcohol ... in fact I honestly don't remember the last time. It's been years.