If the swelling is significant enough, I'd guess the cough is an indicator it's affecting her breathing or swallowing. It also could indicate a parasite called gapeworm, though I have little personal knowledge of it or know what to trerat it with specifically. My go-to for parasites is the pour-on Ivermectin from the cattle section of the feed store. I don't know how well Safeguard does for gapeworm, IF that's what this is. It certainly couldn't HURT, if the issue is actually a parasite. I'd quickly follow it up with Ivermectin, though - in a week or so. Then, since you need to dose twice with whatever you use, you might wwant to redose with Safeguard, then with Ivermectin, once again, to catch any eggs that have hatched. Of course, if it's an infection or reaction from a bite or sting, or if it's a cyst or tumor, neither of those will help. So, we need a closer look at what's going on!
You need to figure out how to handle them, though, especially to treat with Ivermectin, as it's given as a few drops on bare skin behind the neck. Perhaps get them at night, after they've settled in to bed. As you get them, you should also check them over very closely for other external parasites, or anything else they might be hiding, especially if they're flighty - that's the best time to look them over.
Chickens are very good at instinctively hiding any issues, whether sickness or injury, until they can't hide them any more, as they're prey animals, and predators go after the weakest-looking in a flock, herd, pack, or whatever species group they're hunting. That means they will do whatever they can to hide any problems they may have, so they don't look like the weakest. Which also means that, if you have flighty birds, you have to work extra hard to get that chance to handle them.
When you DO get the ones with the bumps, examine them extra-closely. Open their mouths (they'll LOVE that

) and look down their throats with a flashlights, to see if you can see anything in the throat. Closely examine the bumps, to see if they might be from bites or bot fly larvae or stings, etc., and try to get pictures of the bumps. Pictures help us try to figure out what the problem might be so we can offer the best advice. Even if it means bringing them inside, and teaming up, with the camera or phone in one pair orf hands, and the bird in the other pair. A towel wrapped around them snugly (but make sure they can still breathe) can help hold them still long enough for treatment, or examination, or pictures.
[Edited a typo]