Appendicitis in children is difficult to diagnose due to the fact that the symptoms are related to other common stomach issues. The current methods of diagnosis, like Alvarado scores, CT scans, and ultrasounds, may consume a lot of time, and they also give rise to issues like radiation risks. Clinical datasets contain noisy, irrelevant data, which could confuse the model from making an accurate decision. To solve these issues, this paper proposes a machine learning model that uses a hybrid feature selection technique called Mutual Information (MI) guided Binary Whale Optimization Algorithm (BWOA). The selected features use the K Nearest Neighbors (KNN) algorithm to determine if a child has appendicitis or not on the Regensburg Pediatric Appendicitis data. The proposed model has outperformed the existing methods because it maintained 97.43% accuracy, 95.52% precision, 98.46% recall, 96.96% F1 score, and an Area Under Curve (AUC) of 0.988 with only 19 of the 57 features. To make the model interpretable, Explainable AI (XAI) through SHAP (SHapley Additive exPlanations) is integrated. These results show that the model selected only the required feature subset, which made it easier and faster to accurately diagnose appendicitis.