Re: clogged tube/chunky pus above tonsil.
hi..yes, those are tonsiliths or tonsil stones.
They're basically a sloughing from the inside of the tonsils of mucus, food, dead cells that form in pockets of the tonsils. If there's continual inflammation or infection, there can be more of it produced. Sometimes it hardens or calcifies and can require surgery if it becomes too large and exacerbates an infection itself.
My opinion, if you have recurring tonsilitis or infection or inflammation, push to have them removed. You'll probably have them forever...unfortunately.
There's lots of information on this site on tonsiliths and tonsil stones...do the search and you'll get tons of ways to clean them, possibly prevent them, etc.
It's all a matter of perspective!