Did you get the baby checked by any Pediatrician? Excessive irritability might be a sign of iron deficiency anemia. It is a prime age for a baby to develop the same. Also yes teething is another reason for him being cranky
Next Steps
Get him checked by a pediatrician for anemia and get a Hemogram and iron studies done as he advises
Health Tips
Give food cooked in iron vessels and add Jaggery in the food