Could be an enlarged lymph node. I'd want the vet to take some fluid from it and check it out for bacteria or cancer cells or whatever it is they check for.
Mr. Darcy's lymph node is enlarged. My vet drained it once, checked the fluid and told me it was blood filled, but nothing was wrong. We do need to do a second round of ABs for bartonella, but I'm not sure what the cause of his lymph node becoming enlarged again is.
Other than lymph node, the pitituary gland is there, so I would want a vet to check out to rule out an issue there.
I do not know if asthma meds would cause an enlargement, but I've never seen a reference to that. But I'm no vet or expert.