Why would a doctor order blood work for a swollen salivary gland?

Look for cause. Blood work could possibly help in aiding in the diagnose of why someone has a swollen salivary gland. Could there be an infectious process going on or an inflammatory process? These are possible answers the physician could be looking for. I hope this helps.
Infection. They are concerned about an infection in the gland, so would order a blood count.
rule out infection. A swollen parotid gland could be caused by mumps, (were you vaccinated?). It could also be caused by a stone impacted in the salivary gland which could lead to an infection. The swelling could also represent a tumor or lymphoma.