They're not-so-fondly known as "allergic shiners."

Probably worth watching. Probably a sign that she's not breathing (and
sleeping) as well as she should. For those of us with highly atopic
children, it's familiar territory. The cough is a clue. I'd get her
evaluated for asthma and allergies. She could be having other subclinical
symptoms (ones that aren't severe enough to be obvious).

BTW, "without medication" is only a good thing if the adverse effects of
the condition are not worse than the adverse effects of the medications.

Mark