Hello Alea,
Vomiting und diarrhoea can be caused by al lot of diffrent reasons. Most oft the time, gastrointestinal infections like bacterial or viral infections are responsible for these symptoms. But also other diseases like an ileus or an organic problem can cause vomiting and diarrhoea.
I suggest you to feed sensitive food for the next days. You can use cooked chickenbreast with rice or noodles, carrots and curd. Feed you dog small portions throughout the day.
Additionally you can give your dog diarrhoe-pastes like "Canikur®" or "Enterogelan plus®". These drugs act antiinflammatory and renew the exhausted intenstinal membrane.
If your dog doesnt get better, continues vomiting or shows additional symptoms, like lethargy or bad general condition, you shoud let him get examinated by a vet.
Best wishes 🐾