Eosinophilic Gastroenteritis: This condition is characterized by the infiltration of eosinophils into the gastrointestinal tract, leading to abdominal pain, nausea, vomiting, and sometimes diarrhea. The description of the pain as feeling like "someone's wringing out a washcloth" could be indicative of the intestinal spasms associated with this condition. Elevated eosinophils in the blood support this diagnosis.

Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease and ulcerative colitis can present with abdominal pain and elevated eosinophils, although the latter is not a hallmark of IBD. The central and lower abdominal pain could be consistent with Crohn's disease, which can affect any part of the gastrointestinal tract.
Gastrointestinal Parasites: Infections with parasites such as hookworms, roundworms, or tapeworms can cause eosinophilia and abdominal pain. The symptoms could vary depending on the type of parasite and the location of the infection within the gastrointestinal tract.
Food Allergy or Intolerance: Certain food allergies or intolerances, especially those involving eosinophilic esophagitis or gastroenteritis, can lead to abdominal pain and elevated eosinophils. The pain description might fit with the diffuse inflammation seen in these conditions.

Appendicitis: Although appendicitis typically presents with pain localized to the right lower quadrant, atypical presentations can occur, especially in the early stages. It's crucial to consider appendicitis due to its potential for severe complications if not promptly treated.
Intestinal Obstruction: This condition can cause severe abdominal pain and could potentially lead to eosinophilia due to the body's response to tissue injury. The "wringing" sensation might be indicative of the intestinal spasms associated with obstruction.
Mesenteric Ischemia: This is a life-threatening condition that can cause severe abdominal pain out of proportion to physical examination findings. While eosinophilia is not a typical finding, the severe nature of the pain and potential for catastrophic outcomes make it a "do not miss" diagnosis.

Eosinophilic Colitis: A rare condition characterized by eosinophilic infiltration of the colon, leading to abdominal pain, diarrhea, and sometimes blood in the stool. It's part of the spectrum of eosinophilic gastrointestinal disorders.
Hypereosinophilic Syndrome (HES): A rare disorder characterized by the overproduction of eosinophils, leading to organ damage. Gastrointestinal symptoms can occur, including abdominal pain, but this diagnosis would require additional systemic symptoms and significant eosinophilia.
Churg-Strauss Syndrome (Eosinophilic Granulomatosis with Polyangiitis): A rare autoimmune condition that can cause eosinophilia, abdominal pain, and gastrointestinal symptoms among a wide range of systemic manifestations. It's a diagnosis to consider in patients with multi-system involvement.