Is any other horse at your barn sick or with the same
symptoms? Or, has your horse been anywhere or exposed to other
horses recently? Since the lumps are on both sides, it would rule out an insect bite or bee sting, so my incination is to say the the lymph nodes/guttural pouches are inflammed. This would indicate some sort of systemic infection. Just like the lymph nodes on our (human)necks get big and sore when we are sick.