When a horse has swelling other than his lymph nodes, this is usually a sign that he has a much more serious case and will need much longer treatment and isolation. And yes, *** strangles can be dangerous if not treated.
Having just been through a nasty outbreak of strangles at our farm, I learned more than I ever wanted to know...
The best treatment: let it run its course and keep all affected horses as well as ANY horses that may have come in contact with affected horses or sick horses' water buckets, equipment or handlers, in isolation. The strangles bacteria is VERY contagious, especially through water or moisture, i.e. water troughs, buckets, snot, and dewy grass.
When strangles is first suspected, a course of antibiotics can be given, but should be halted as soon as any signs of abscessing in the throat is detected. This will allow the abscesses to mature and burst, which is what you want. You can even puncture them and drain them or have your vet to do it if they are very slow in rupturing.
Regular strangles is a messy PITA and the associated quarantine is a MAJOR PITA but as a whole, it is a lesser type of horsey disease. It, in general, is not fatal and does not have any lasting effects. Just is truly gross. Monitor temperatures of all horses on the farm twice a day -- a temp spike above 101/102 tells you the horse has likely gotten the bacteria and needs to begin antibiotics.

Solaris -- 16 hh Appendix Quarter Horse = MY DREAM COME TRUE!