Automated diagnosis of eczema using images acquired from digital camera can enable individuals to self-monitor their recovery. The process entails first segmenting out the eczema region from the image and then measuring the severity of eczema in the segmented region. The state-of-the-art methods for automated eczema diagnosis rely on deep neural networks such as convolutional neural network (CNN) and have shown impressive performance in accurately measuring the severity of eczema. However, these methods require massive volume of annotated data to train which can be hard to obtain. In this paper, we propose a self-supervised learning framework for automated eczema diagnosis under limited training data regime. Our framework consists of two stages: i) Segmentation, where we use an in-context learning based algorithm called SegGPT for few-shot segmentation of eczema region from the image; ii) Feature extraction and classification, where we extract DINO features from the segmented regions and feed it to a multi-layered perceptron (MLP) for 4-class classification of eczema severity. When evaluated on a dataset of annotated "in-the-wild" eczema images, we show that our method outperforms (Weighted F1: 0.67 $\pm$ 0.01) the state-of-the-art deep learning methods such as finetuned Resnet-18 (Weighted F1: 0.44 $\pm$ 0.16) and Vision Transformer (Weighted F1: 0.40 $\pm$ 0.22). Our results show that self-supervised learning can be a viable solution for automated skin diagnosis where labeled data is scarce.