Salivary gland swelling on both sides. what could cause this?

Possible mumps: Bilateral obstruction of the glands is highly unlikely, so if you are sure it is the salivary glands (most likely parotid gland) then mumps would be one of the first conditions to rule out in a differential diagnosis.

Possible stone block: This could be a salivary gland blockage. Usually this blockage can cause the gland to swell since the saliva cannot proceed through the duct into your mouth. This type of swelling usually comes and goes and the blockage could be in the gland or in the duct itself. If this continues, you can do damage to the glands. Please go see your dentist.

Mumps? other?: See your physician to first see if it's really your salivary glands that are swollen and secondly, what's causing the swelling. It would be very unlikely to have bilateral swelling of your salivary glands. One thing that can cause this is having the mumps. If your physician cannot determine the cause, he\she may refer you to an oral surgeon for a consultation.