When I had a wisdom tooth out, the surgeon removed a white bump from the underside of my tongue. This was more tender than the tooth removal. Well, when the lab results came back, he said it was a plugged salivary gland. Cool, nothing serious. But it keeps coming back. Gets a little sore. Sometimes I can break it, but I know I shouldn't. Anyone else familiar with these?
Obstruction to the flow of saliva in your submandibular glands occur probably because stones have formed. If left untreated, infection and abscess may occur. If you can squeeze them out, great - you've saved yourself a trip to the dentist. Usually, the dentist will try to squeeze them out. If unsuccessful, then surgery may be indicated.
Okay - Unfortunately I've learned a lot about salivary glands the hard way due to personal experience lately. It's not clear from your post - was the white bump on the floor of your mouth or actually on the underside of your tongue? If it's on the tongue itself it is probably just a minor plugged salivary duct or mucocele. I have one of those on the side of my cheek. It fills up regularly almost like a blister and I can pop it. It is painless (but it may hurt like crazy if he cut the area out! - the inside of the mouth is very sensitive!) My ENT and dentist have suggested leaving it alone since mine isn't that big and does not really bother me. They said if they did remove it, it could very likely recur but was nothing to worry about.
On the other hand, if the swelling is on the floor of your mouth, I agree with the other posters that it is probably a stone in the submandibular gland. I have one of these also - lucky me! You will notice swelling of the gland under your chin when you eat. It can be VERY painful if it gets infected. This is treated with antibiotics if infected, and lots of water/sour candies/lemon juice/pickles, anything to stimulate saliva flow. These are very common and, if you are lucky, and most people are, the stone will pass on its own. Or your dentist or doctor may be able to push it out the duct in the office. Unfortunately, my stone is deep in the gland itself and can't be reached. If they can see it they can remove it with a small surgical in-office procedure. If not, there is no option other than to remove the whole gland - which is where I am at now.
Check with your dentist and see if it was a blockage of just a minor salivary gland or the submandibular gland. That will give you an idea of how to proceed. Also, my dentist sent me to an ENT for his option - always an option if you're not sure.