It's possible that the pain around your salivary glands reflects your sodium-iodide symporters needing support. Try Vitamin C 1 gram three times a day.
It's also important to use either ATP Cofactors or a generous amount of Vitamin B2 and Vitamin B3 (as inositol hexaniacinate).
It's early days with your Iodine supplementation, too early to know what effects it may have for you.