
Is her mouth sore that is stopping her eating? Was there only the stick in her mouth and a piece hasn't broken off and gone down into her oesophagus/stomach or bowel, if these excessive sounds from the gut continue you need to get her back to the vet for a check over, don't know if sticks show up on Xray or scan.
You may have to give her sloppy food for a few days so she can lap rather than chew.
Eating less than she normally does can cause a build up of bile leading to nausea/vomiting and in turn no interest in eating, as the day goes on and she takes in small amounts things will settle explaining why later in the day she has more appetite.
Hope she gets back to normal soon