I agree, I do not think that's a heave line.
I had a heavey horse in the barn once and she did not develop the heave line until the condition was quite chronic and really interfered with being able to work. That was after she stopped responded to oral steriods to manage the acute outbreaks.
The "heave line" is caused by the horse using their auxilary muscles to assist respiration. The corollary in humans is that people with emphysema or other COPDs are usually skinny but barrel chested.
If that was a heave line, you'd see her muscles contract and relax along that line as she breathed. Because she's be using the intercostal muscles (the ones between her ribs) to help breathe.
If she has allergies, you know what you need to do - maximize turnout and graving, minimize stall time and time in dusty environments, feed the cleanest hay you can find (timothy is the usual choice in my area) dampened if necessary, use steriods sparingly to manage acute episodes.