Skin-disease diagnosis from dermoscopic images is obstructed by small datasets and large intra-class variability. This paper proposes a classification method that integrates a bilinear Convolutional Neural Network (CNN) with a constrained triplet network using a matrix-similarity based joint loss function to improve skin disease classification performance. The bilinear CNN captures complex spatial correlations by computing the outer product of feature maps from two distinct CNN streams, followed by bilinear pooling to obtain second-order interactions, while a constrained triplet loss encourages embeddings from the same class to group closely and enforces separation between distinct classes. A similarity matrix derived from softmax outputs guides a weighted softmax loss. Experiments on the benchmark HAM10000 and ISIC-2019 datasets show that the proposed method achieves 93.37% accuracy on HAM10000 and 93.78% on ISIC-2019, which outperform recent state-of-the-art models. This framework demonstrates the benefits of combining metric learning with second-order feature pooling for robust skin disease classification.