Chemotherapy-induced mucositis or proctitis: This is a common side effect of chemotherapy, especially with agents like paclitaxel and carboplatin. The timing of the symptoms after the initiation of chemotherapy and the absence of fever or neutropenia support this diagnosis.

Radiation proctitis: Although the question does not explicitly mention radiation therapy, it is a common treatment modality for uterine cancer. If the patient received radiation, this could be a likely cause of her symptoms.
Thrombocytopenia or coagulopathy: Chemotherapy can affect platelet counts or coagulation factors, leading to bleeding. Even without neutropenia, thrombocytopenia could be present.
Gastrointestinal infection: While there's no fever, certain infections (e.g., Clostridioides difficile) could cause hematochezia without systemic signs of infection, especially in immunocompromised patients.

Lower GI tract tumor or metastasis: Although less likely given the recent chemotherapy, a new or growing tumor in the lower GI tract could cause bleeding. This would be critical to diagnose as it could significantly alter the treatment plan.
Bleeding disorder: An undiagnosed bleeding disorder could be unmasked by the stress of chemotherapy or the cancer itself. Missing this could lead to significant morbidity or mortality.
Typhlitis (neutropenic colitis): Despite the absence of neutropenia, typhlitis is a potentially life-threatening condition that requires prompt diagnosis and treatment. Its presentation can sometimes be atypical.

Vasculitis: Certain types of vasculitis can cause GI bleeding. This would be an unusual presentation but should be considered if other causes are ruled out.
Intussusception: Although more common in younger children, intussusception can occur at any age and could be a cause of hematochezia. It might be related to a lead point such as a tumor.
Hemorrhoids or anal fissures: These are less common in children but could be considered, especially if there's a history of constipation or straining during bowel movements.