Hellion,
I went thru the exact thing you are now in my week3-4? of recovery.
I had thick nasty phlem/mucus that just hung out right above the back of my uvula. Any attempt to dislodge equaled a trip to the bathroom to vomit. My stomach got weak and the gag reflex became even easier to trigger.
All I can say is it will pass. I tried Mucinex and it didn't really help. Its one of those every 4 days things for me. It seemed during recovery there was a new and different battle every 4 days. I remember soda water and ginger ale being my friends during this time frame. They both provided minor assistance.
This will pass in a few days, I think it was about 10 total days like this for me.