My horse has a lump and serous drainage under her jaw.?

Sounds like a infected lymph node and worst case scenario strangles. I have had my hands in strangles before and it was not fun. I also learned that the internasal strangles shot can cause a mild case of strangles. If you have strangles it is always followed by a high fever. I know first hand that it can be up to 3 months incubation period. I know this from a mare and foal returning from a infected farm. They never got ill and I did not want them back so soon but they were allowed back and 6 weeks later it broke out thru my weanlings. Now I have also had swollen lymph nodes occur from strangle shots and open. My vet told me it wasn't secondary! That ended up being bullcrap so don't let anyone tell you different. I again had 3 horses affected by the mare that was juicing everywhere. I do not give internasal strangles anymore for this reason and not to mention how much the horses hate it and how many times I almost got severely creamed for slapping legs. My point is, you probably only have a infected lymph node if you have not exposed your horse recently to the strangles shot. Like I said, Strangles comes with a high fever. Take a syringe without a needle on it and flush the hole with betadine. You can also go to your farm store and get a triple antibotic thats used on cows for mastitis. Its in a syringe but you want to flush the wound first. Keep a eye on him for safety reasons and if it was me, not knowing your horse like you do, I would quarantine him intill it stopped draining. But you know where your horse has been. I just reread your post and just because she has had the strangles shot, does not mean squat! If you have given it recently I would contribute it to that. When I have had them react to it, it was anywhere from 2-4weeks after the nasal. The reactions from the shots were no fever, just a small abscess that would open and drain. Wishing your horse well!!