Do you have amalgam (silver) fillings? They contain mercury and recent studies show that we can be poisoned by them.
Many people have been "cured" by having these replaced with the new filling materials.
Wishing you the best
If you have a Mayo Clinic in your area or even if you have to drive or fly there, I would go there, they are are the best, check to see if your insurance is accepted there first. They have all the Doctors on one campus, otherwise, you could be going to Doctor after Doctor and that could take months and months. You definitely need a specialist, a regular GP is not your answer.
IT may take a team of doctors to solve this for you and again the Mayo has all those things.
Best of luck to you. From SedonaMom
I can only say that I am so sorry you have this condition. I have a little book titled: The Best of Health and on page 165 it says this about Too Much Saliva.
"It's possible that you just have trouble swallowing. That problem, which people often don't notice, can cause saliva to collect in your mouth, making you think your saliva glands are working overtime. an ear, nose, and throat specialist can test you swallowing reflex, which can be damaged by several neurologic or muscular disorders. if the reflex is normal, you should probably see a dentist who specializes in salivary-gland disorders - usually at a university medical center or large hospital - who can measure your saliva secretion. If excessive salivation is the problem, doctors should check for an underlying cause, such as a drug side effect, gastroesophageal reflux, or a rare effect of diabetes".
Sorry I couldn't answer in my own words. I hope this information is helpful.
Wishing you the best