Irritable Bowel Syndrome (IBS): Given the patient's symptoms of epigastric pain, postprandial discomfort, and early satiety, which are common in IBS, and the fact that other tests have come back normal, IBS is a strong consideration. The development of right side pain could be a manifestation of IBS, which often involves abdominal pain that can shift locations.

Functional Dyspepsia: This condition is characterized by persistent or recurrent upper abdominal pain or discomfort that is not explained by other pathologic conditions. The patient's symptoms of epigastric pain and early satiety align with functional dyspepsia, especially since the EGD and other diagnostic tests were normal.
Gallbladder Disease: Although the HIDA scan was normal, gallbladder disease (e.g., biliary dyskinesia) could still be considered, especially with the new onset of right side pain. The rash could potentially be related to a systemic response to gallbladder disease, although this is less common.
Inflammatory Bowel Disease (IBD): Despite the normal appearance of the gastric and duodenal mucosa on EGD, and the absence of intestinal metaplasia, IBD (Crohn's disease or ulcerative colitis) could still be a consideration, especially if the rash is suggestive of an extraintestinal manifestation of IBD.

Hepatitis: Although less likely given the normal liver function tests are not mentioned, hepatitis could cause right upper quadrant pain and a rash. It's crucial to rule out hepatitis due to its potential for serious complications.
Pancreatitis: Acute or chronic pancreatitis could explain the abdominal pain and potentially the rash if there's a systemic inflammatory response. This diagnosis would be critical to identify due to the potential for severe complications.
Lymphoma: Given the patient's age and the presence of H. pylori, which is a risk factor for gastric lymphoma, it's essential to consider this diagnosis, although it is less likely without specific findings on EGD or imaging.

Eosinophilic Gastroenteritis: This rare condition involves eosinophilic infiltration of the gastrointestinal tract and could explain the patient's symptoms, including the rash if it's related to an allergic or eosinophilic reaction.
Scleroderma: This autoimmune disease can affect the gastrointestinal tract, causing dysmotility and potentially explaining some of the patient's symptoms. However, scleroderma typically presents with skin changes (tightening of the skin) and other systemic symptoms.
Whipple's Disease: A rare, systemic bacterial infection that can cause malabsorption, weight loss, and abdominal pain, among other symptoms. It's extremely rare and would be a consideration only if other diagnoses are ruled out and there are specific findings suggestive of Whipple's disease.