Phenergan is for allergic disorders, anaphylaxis, antihistamine and hypersensitivity disorders. It is not recommended you use this for nausea.
If he becomes lethargic or you notice blood in the stool or vomit, he needs to see his vet promptly. As this is a sign of serious illness including a parasite infection or a blockage among other things. This sounds like a case of upset stomach. You can self treat this at home unless any of the above symptoms start presenting.I would start him on a bland diet of boiled chicken and rice to help settle his stomach.(1 part skinless chicken Breast to 3 parts white rice) If he refuses to eat it mash it up and apply small amounts along the jaw line to force him to eat.I am concerned with him becoming dehydrated as this is quite serious with dogs. I recommend giving him unflavored pedilayte to replace the electrolytes. If he refuses this as well you can use a small syringe to force fluids into him.You can also give him One teaspoon of Pepto Bismol per 10 pounds of body weight for faster relief.Walter
Is the label printed from the pharmacy? If so sometimes a vet can use a certain medication for something that it is not typically made for. This is a strong drug to be used for nausea but if your vet planed on its use for this then it can be used.
Many drugs are used for conditions not listed in its general usage directory. While the phenergan is not typically used in nausea for dogs the vet can prescribe it for this if he feels it will be helpful.