Those are lymph nodes. They swell when they are fighting infection.
I don't understand the level of uncertainty about what is going around this barn. Veterinarian(s) have been there, drugs are being dispensed. What are they treating? I'd have a long talk with the vet tomorrow, in person and try to get some solid information, I wouldn't settle for what it might be.
You understand then. It is so frustrating. The owner thought Okie had strangles. The house vet said no, rhino. Then horses for sure that were vac get sick. My vet didn't tell her anything. I will corner him tomorrow for answers. Yes, I want them treated and glad Okie responded so well, but what the hell is going on? I'm not blaming anyone or trying to cause problems. People and animals get sick. It happens. I just want to know what I'm dealing with.