Hi thanks for the question

Lip licking is a sign of nausa so your vet is right.

I would not with hold food if there is no vomiting however I would recommand putting her on a bland diet of boiled chicken and rice. Please rinse the chicken after boiling to remove all fat. Feed small meals 3 times a day. I would do this for 3 days on day 4 I would replace 1 of the small meals with her regular kibble, day 5 2 of the meals can be regular kibble day 6 she should be on regular feed schedule with her normal kibble.

You can give 1/4 tablet of pepcid ac 2x daily for 2 days this will help control the stomach acid that may be adding to the nausa.

I would mix a small amount of infant pedialyte to her water to help keep he sugar and electrolytes stable

Always avoid diet changes and people food with small dogs as this can lead to pancreatitis

ok, I think she is just enjoying your attention and being babied, I suspect she is drinking when you are not looking. This is very common

Her gums are moist and she is urinating. If her only water intack was coming off your finger I would expect to see signs of dehydration as she could not get enough off of your finger to keep her properly hydrated.