>>52847537Asthma seems likely. Though if they do confirm any sickness, they'll probably just say she's sickly without giving specifics. But given how easily she gets winded and how much she complains about the school stairs, asthma does feel likely.
I also wonder about her arm, since I have a feeling she actually needs the brace and it isn't just an accessory. She can't throw a Poké Ball to save her life, and she often uses her left hand to support her right arm in battle. She also seems to be in pain when terestallizing her Pokémon.
Nemona's body just seems to be a complete mess all around, and I'm hoping GF expands on that in the DLC.