To further clarify my guess, the tumour can be small, and grow slow, but at some point the saliva is blocked, and the resultant backup is quick.
There are many reasons, injury perhaps the most common, that a salivary gland may be blocked. All of the aforementioned guesses can do so. Antibiotics may help if it's infection related, or they may help by preventing an infection so the body can heal the cause naturally. In the end, if antibiotics don't help, further diagnostics are needed to proceed. I would ask your vet about this, or if you feel uncomfortable asking your vet to pursue this manner or for a second opinion, by all means look for another.
ARAV is a good place to start.
Ian