Cat won't eat and rarely drinks; vet can't find anything wrong?

You need to find another vet. There's something making you cat sick. Could be virus or bacterial, maybe parasite. I do believe you need a second opinion. A healthy cat would eat and drink. Vomiting could be several reasons, fur or eating something it shouldnt or even the brand of food. My cat throws up bc of feline leuakemia. Best advice is to get a second opinion, hope your baby gets better.