My puppy ate a stick. Should I go to the vet if it hasn't passed?

I can certainly understand your concerns about Finn's stick ingestion, but the good news is that it sounds as though he's still doing very well at home. Stick ingestion is a bit of a tricky situation. Even if you had taken Finn to his vet immediately after he'd eaten the stick, your vet would likely have advised against inducing vomiting. The induction of vomiting of potentially sharp objects risks perforation of the esophagus, which is extremely dangerous. The only other ways to get the stick out are a) wait for it to pass or b) surgically remove it. At this point, the fact that Finn is doing well at home (namely eating, drinking, and acting normally without any vomiting or diarrhea) indicates that it's still more than reasonable to simply wait and give him more time to pass it. While I can't definitively tell you that surgery is absolutely not indicated without having examined Finn, it doesn't sound as though it's something that you need to urgently pursue by taking him to the vet. For the time being, I think it's reasonable to continue monitoring Finn closely at home. If you notice anything change, such as a loss of appetite, lethargy, vomiting, retching, gagging, or diarrhea, be sure to take him to see his vet right away. Otherwise, feeding him a bulkier diet, such as bread and rice, pumpkin, and boiled chicken may help him to pass the stick through his stool a bit more efficiently. I hope this helps and that everything goes well!