Viral Gastroenteritis: This is the most likely diagnosis given the symptoms of cough and vomiting. Viral gastroenteritis is a common condition that can cause these symptoms, especially in young adults. The cough could be related to the vomiting or a concurrent viral upper respiratory infection.

Influenza: Influenza can cause cough, vomiting, and other systemic symptoms like fever and body aches. Given the acute onset, this is a plausible diagnosis.
Acute Bronchitis: This condition can cause a cough and might be accompanied by vomiting if the cough is severe enough to trigger a gag reflex.
Pneumonia: Although less common, pneumonia should be considered, especially if the patient has a high fever, difficulty breathing, or chest pain.

Pulmonary Embolism: Although rare in young adults without risk factors, pulmonary embolism can present with cough and vomiting (if the patient is experiencing significant distress or pain). It's crucial to consider this diagnosis due to its high mortality rate if untreated.
Appendicitis: While the primary symptom of appendicitis is abdominal pain, vomiting is common, and cough could be a referred symptom or from a concurrent condition. Appendicitis requires prompt surgical intervention.
Meningitis: If the patient has a severe headache, stiff neck, or altered mental status along with cough and vomiting, meningitis must be considered due to its potential for severe consequences if not promptly treated.

Cystic Fibrosis Exacerbation: If the patient has a history of cystic fibrosis, an exacerbation could present with these symptoms, especially if there's an underlying respiratory infection.
Foreign Body Aspiration: Although more common in children, aspiration of a foreign body can occur in adults and might present with sudden onset of cough and potentially vomiting.
Eosinophilic Esophagitis: This condition can cause vomiting and might be associated with a cough if there's an esophageal obstruction or if the condition triggers a gag reflex.