[souffle]

Hamsters don't vomit so it won't be that.
Chin wetness is due to drooling which can be caused by bottle chewing, teeth problems, pouch problems and they sometimes drool when they are warm.
Check the teeth are the correct length, not splayed and meet properly. Feel the pouches for stuck food in there or any lumps or bad smell to the breath.
If she bottle chews I would change to a bowl and see if the wetness stops.