Thanks for all your input and suggestions!
I asked a few Japanese friends and they replied as follows:
Probably 目が覚めたas in she got so scared she became wild awake
We say "目が冴える(めがさえる)" when we become wide awake.
I'm thinking the "correct" answer won't necessarily make a difference, since I'm thinking the meaning is more or less "I was awake a lot!" due to the context of the manga, where the child has night terrors and wakes up in the middle of the night due to insecurity issues. The father knows this, but also has a history of being beaten on by his elder sister, who was watching the child, so misinterprets "I woke up a lot!" to mean something more like "I was so scared I couldn't sleep!"
Or something.
「めっ!」された seems plausible as well, but don't know why the mangaka wouldn't have just used a young-kid-speech-impediment version of 怒られた or 叱られた if that was what she wanted.
It is a great mystery!
Fudgey-translatey version in the final script: "Yeah. Shio lotta wakey-wakey!"