B.C.
Stuffy nose is more of an adenoids thing than tonsils but they are usually removed at the same time when a tonsillectomy is performed.
My son's tonsils were not infected - he had no fever or signs of illness.
They simply swelled to the point where they interfered with his breathing while he slept and swallowing - they became an obstruction.
They were huge fleshy marbles at the back of his mouth that almost touched each other closing off his throat.
We tried shrinking them with steroids but as soon as the series was finished they ballooned right back up again.
There really was no other choice for us - they had to come out (and they did the adenoids at the same time).
After a week of recovery he was eating and sleeping SO MUCH BETTER than he had been.
The snoring was gone immediately and the dark circles under his eyes vanished (he could not sleep well when he could not breathe).
See what the ENT has to say.
Personally, I've never heard anyone say that having the tonsils/adenoids out didn't help.