I tend to think it is not a bug that made her sick. Chloe eats spiders, flies, pill bugs, and has even eaten snails (yuk!)
Bugs are primarily protein and calcium (I know, gross anyway) and are supposed to be very nutritious (even for humans! I know, I could puke at the thought!) I can't imagine that there is anything about a waterbug that would make her sick.
Now, =I= might get sick just looking at one...