Your child could indeed be suffering from a gastrointestinal infection which may be the cause of vomiting and diarrhea. Excessive loss of salts and water from the body could give rise to dehydration, causing your child to feel tired. Please take her to the emergency room of a hospital with pediatric facilities, and get her assessed without delay. As of now, maintain proper hydration by giving ORS (oral rehydration solution) prepared by mixing a full sachet in a litre of plain water. Do not give milk for a week although you may give your child plenty of curd or yogurt since it contains beneficial bacteria.