That the chick can't hatch and it is throwing up and this membrane can't come off maybe?
I've been raising chickens my entire life and this isn't the normal wet and sticky it's different. It's like rock hard. It's eye is actually completely smash and messed up bcus of the membrane not from me pulling btwOh, I thought you said you already took it out and tried cleaning it. Maybe just try clearing it's mouth with an eye dropper or something so it doesn't choke. I wouldn't worry about what's on its body. They all come out kinda wet and icky.
EDIT: maybe a better picture would help clarify what is going on