Re: clogged tube/chunky pus above tonsil.
Good you went to the ENT. I suspect you'll be more prone to them, especially since you're having issues with your ear/sinuses.
I'd suggest to try Sudafed (not the high dosage stuff, however) to see if that can help, and a sinus rinse such as the NeilMed squirt bottle that you mix yourself.
The popping exercise would be eustachian tube related....both what I suggested can help.
Keep an eye on your tonsils and maybe invest in a water pik (if you have room in your bathroom)...I read about others who use that to clear out tonsils.
Feel better soon.
It's all a matter of perspective!