Functional Dyspepsia: Given the lack of relief with omeprazole, a medication typically used to treat gastroesophageal reflux disease (GERD) and peptic ulcer disease, and the absence of significant laboratory abnormalities, functional dyspepsia is a plausible diagnosis. It is a common cause of chronic nausea in young adults, characterized by recurring symptoms of upper abdominal discomfort or pain that are not explained by other medical conditions.

Gastroparesis: This condition, characterized by delayed stomach emptying, can cause nausea, especially after eating. It might not be directly indicated by the labs provided but could be a consideration given the chronic nature of the nausea.
Irritable Bowel Syndrome (IBS): Although primarily known for causing abdominal pain and changes in bowel habits, some patients with IBS may experience nausea. The normal labs and lack of response to omeprazole make this a possible, though less direct, cause.
Anxiety or Depression: Psychological factors can contribute to gastrointestinal symptoms, including nausea. The chronic nature of the symptoms and the lack of a clear physical cause might suggest an underlying psychological component.

Pregnancy: Although not directly suggested by the information provided, pregnancy is a critical diagnosis to rule out in any female of childbearing age presenting with nausea, due to its potential impact on both the mother and the fetus.
Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease and ulcerative colitis can cause chronic nausea among other symptoms. The normal ferritin and iron concentration do not rule out IBD, as these can be affected by many factors, including the disease's activity and the patient's dietary intake.
Celiac Disease: An autoimmune reaction to gluten, which can cause nausea, abdominal pain, and changes in bowel habits. It's essential to consider, especially if the patient has not been tested for it, as it can have significant implications for management and quality of life.

Zollinger-Ellison Syndrome: A rare disorder characterized by excessive gastric acid production due to a gastrin-producing tumor. The lack of response to omeprazole might raise suspicion, although it is much less common than other causes of nausea.
Eosinophilic Gastroenteritis: A rare condition involving eosinophilic infiltration of the gastrointestinal tract, which can cause nausea, abdominal pain, and other symptoms. It would be considered if other diagnoses are ruled out and if there are specific indicators such as significant eosinophilia or atopic history.
Mitochondrial Disorders: Certain mitochondrial disorders can affect the gastrointestinal system, leading to symptoms like nausea. These are rare and would typically be considered if there are other systemic symptoms or a family history suggestive of a mitochondrial disorder.