What you are getting from tonsil
is called debris -comes out from crypts of it. Some people do get this. One crypt near upper part of tonsil is bigger. From here it comes out. It is formed by epithelial cells
, food particles and common bacteria found in mouth.
It is harmless and apart from throwing it out when it pops out, nothing need be done. But if you are very much bothered by it, removal of tonsils by surgery will solve that problem.
Nasal polyps are not related to your tonsil problem.
You can show to an ENT specialist
who can examine you and tell you for sure whether you have nasal polyps and he will advise you regarding further management of it if you have polyps.
by managing it, take regular exercise and do meditation
Avoid taking chocolates and other migraine precipitating things.
Avoid sleeping too much or less.
Any irritating lesion in head neck area including ENT or eye problem need to be treated -as these can increase the severity and frequency of migraine attack.
See a good GP/Physician (internist) for migraine prophylaxis that is long term medication to prevent migraine attacks as total cure for it is not likely.
Wish you good health.