Viral Gastroenteritis: This is often caused by norovirus or rotavirus, and while a skin rash is not the most common symptom, some viral infections can cause a rash. The combination of gastrointestinal symptoms with a rash could be seen in certain viral infections, making this a plausible initial consideration.

Food Poisoning (Bacterial): Certain bacteria like Staphylococcus aureus, Salmonella, or E. coli can cause food poisoning, which may include symptoms of gastroenteritis. Some of these infections can also be associated with skin manifestations, such as a rash, especially if there's an allergic component or toxin involved.
Allergic Reaction: An allergic reaction to food can cause both gastrointestinal symptoms (like diarrhea and vomiting) and skin symptoms (like a rash or hives). This is a common scenario and should be considered, especially if the patient has a known food allergy.

Hemolytic Uremic Syndrome (HUS): This condition, often associated with E. coli infections (especially E. coli O157:H7), can cause severe gastroenteritis and is sometimes preceded by or associated with a rash. HUS can lead to kidney failure and is life-threatening, making it crucial not to miss.
Streptococcal Infections: Certain streptococcal infections, like Scarlet Fever, can cause a rash and gastrointestinal symptoms. These infections require prompt antibiotic treatment to prevent complications like rheumatic fever.
Meningococcemia: Although less common, Neisseria meningitidis infections can cause a rash (often petechial or purpuric) and gastrointestinal symptoms, among other systemic symptoms. This condition is life-threatening and requires immediate medical attention.

Erythema Infectiosum (Fifth Disease): Caused by Parvovirus B19, this condition is characterized by a distinctive "slapped-cheek" rash and can be accompanied by mild gastrointestinal symptoms in some cases.
Kawasaki Disease: An acute febrile illness that predominantly affects children, characterized by fever, rash, and other specific criteria. Gastrointestinal symptoms can sometimes be part of the presentation. It's a rare but important diagnosis due to its potential to cause cardiac complications if not treated promptly.