I am surprised that the antibiotics have had zero impact. I would have expected something. So that makes me wonder if it is just the wrong antibiotic for the infections ( there are gram positive and gram negative bacteria each requiring different antibiotics) , or if it is not an infection at all.
The surgery to remove a small salivary gland is a minor procedure, and the mouth recovers amazingly fast compared to other parts of the body. I think I would want two things, a head and neck CT/or MRI with contrast, to see that this is all things are, and this is all that is going on. The second thing is that the excised material to be sent for a full pathology work up, so that you will have an unambiguous answer to determine what it was.