I think a bit more questioning is in order.
The OP shows that they live in New Jersey - I heard from an aquarist in New York, that seasonal tropical "waifs" are already showing up in these waters...notably very small Chaetodon ocellatus. So, given the location, and that the fish arrived in a water bottle (implying self-collected) I'm pretty certain that this fish is a juvenile spotfin butterflyfish, besides, that's what it looks like, juvenile sedentarius have white pelvic fins, not yellow like in the image.
While C. sedentarius are NOT obligate coral-feeders (they are actually more zooplanktivores, and do very well in captivity) C. ocellatus are a problem feeder, they aren't obligate coral feeders either, but they just don't adapt to prepared foods well. My guess is that they feed on feather dusters, urchin tube feet, or other esoteric foods in the wild.
So - jmaneyapanda is correct, these little guys need almost constant food, I would try HUFA enriched live baby brine shrimp, maybe live tubifex (black) worms, maybe mussel on the half shell.
Good luck, but these can be real heartbreakers......
Jay