Significant health concerns are associated with skin diseases, and accurate and timely diagnosis is essential for effective treatment and patient management. To improve the classification of cutaneous diseases, we propose a novel hybrid system that incorporates the strengths of random forest (RF) and deep neural network (DNN) algorithms. The system employs data augmentation and balancing techniques to enhance model performance and generalizability. The HAM10000 dataset of diverse dermatoscopic images is used for training and evaluation in this study. In the hybrid system proposed, the RF model provides an initial diagnosis based on patient-reported symptoms, while the DNN analyzes images of skin lesions, resulting in more precise and efficient diagnoses. Using hyper-parameter optimization, we fine-tune the system for optimal performance. The evaluation demonstrates the accuracy of the hybrid model, which achieves a classification accuracy of 96.8% overall. According to our findings, the hybrid system demonstrates exceptional efficacy in six of seven skin disease classes. Variations in sensitivity and reliance on data quality and quantity are however cited as limitations. Nevertheless, this hybrid system has the potential to revolutionize skin disease diagnosis and treatment.