The skin of an individual serves as the primary defense mechanism for safe guarding vital organs in the body. Although this barrier effectively protects internal organs from a variety of threats, it is still prone to damage from viral, fungal, or dust-related illnesses. Even minor skin injuries possess the potential to escalate into more severe and hazardous conditions. A prompt and precise skin disease diagnosis becomes crucial in expediting the healing process for individuals grappling with skin-related issues. The objective of this study is to develop a system based on Convolutional Neural Network (CNN) that can accurately identify various skin diseases. The proposed architecture, known as TFFNet (Two-Stream Feature Fusion Network), integrates two simultaneous modules featuring a Self-Attention (SA) block. We employ Self Attention-Convolutional Neural Networks (SACNNs) and Depthwise Separable Convolution (DWSC) to establish a diagnostic system for skin diseases. In this method, two separate CNN models are joined together, and two parallel modules (M1 and M2) are added. This greatly reduces the total number of trainable parameters. In comparison to other deep learning methods outlined in existing literature, the proposed CNN exhibits a notably lower number of learned parameters, specifically around 7 million for classification purposes. The skin disease classification was carried out on three datasets—ISIC2016, ISIC2017, and HAM10000. The model achieved testing accuracies of 89.70%, 90.52%, and 90.12% on each respective dataset.