Viral Gastroenteritis: This is the most likely diagnosis given the symptoms of vomiting and runny nose, which are common presentations of viral infections affecting the gastrointestinal and respiratory systems.

Influenza: The combination of vomiting and runny nose could be indicative of influenza, especially during flu season, as it can cause both gastrointestinal and respiratory symptoms.
Food Poisoning: This could be another likely cause, especially if the patient has recently consumed contaminated or spoiled food, leading to vomiting.
Common Cold: Although primarily a respiratory infection, the common cold can sometimes lead to gastrointestinal symptoms like vomiting, especially in adults.

Appendicitis: Although less common in presentation with runny nose, appendicitis can cause vomiting and should not be missed due to its potential for severe complications if not treated promptly.
Pneumonia: If the runny nose is accompanied by other respiratory symptoms like cough or difficulty breathing, pneumonia should be considered, as it can be life-threatening, especially in older adults.
Dehydration and Electrolyte Imbalance: Not a disease per se, but a critical condition that can arise from prolonged vomiting, requiring immediate attention to prevent serious complications.

Rabies: Extremely rare, but if the patient has been exposed to animals that could potentially carry rabies, this diagnosis should be considered, especially if there are neurological symptoms accompanying the vomiting and runny nose.
Botulism: Another rare condition that could present with vomiting among other symptoms like difficulty swallowing or speaking, and is critical to identify due to its potential for severe outcomes if not treated.