Hi, welcome to the forum, it is unlikely to allergy to dryerase markers. The symptoms are not typical of allergy. Lymph nodes of head and neck enlargement need careful evaluation. Firstly it may be due to infected foci. It is important to rule out the cause. The possibilities are infection beneath skin involving deeper structures such as parotitis due to mumps, parainfluenza and bacterial infections, particularly Staphylococcus aureus.
Noninfectious factors which can be responsible for lymph nodes enlargement includes salivary calculi, tumors, sarcoid, Sjogren's syndrome and head and neck cancer. Infection needs appropriate antibiotic coverage and drainage procedure may be required if abscess is formed. I suggest you to consult physician/surgeon to rule out the cause and appropriate treatment. Take care and regards.