Reliable and effective diagnostic systems are of vital importance for COVID-19, specifically for triage and screening procedures. In this work, a fully automatic diagnostic system based on chest X-ray images (CXR) has been proposed. It relies on the few-shot paradigm, which allows to work with small databases. Furthermore, three components have been added to improve the diagnosis performance: (1) a region proposal network which makes the system focus on the lungs; (2) a novel cost function which adds expert knowledge by giving specific penalties to each misdiagnosis; and (3) an ensembling procedure integrating multiple image comparisons to produce more reliable diagnoses. Moreover, the COVID-SC dataset has been introduced, comprising almost 1100 AnteroPosterior CXR images, namely 439 negative and 653 positive according to the RT-PCR test. Expert radiologists divided the negative images into three categories (normal lungs, COVID-related diseases, and other diseases) and the positive images into four severity levels. This entails the most complete COVID-19 dataset in terms of patient diversity. The proposed system has been compared with state-of-the-art methods in the COVIDGR-1.0 public database, achieving the highest accuracy (81.13% ± 2.76%) and the most robust results. An ablation study proved that each system component contributes to improve the overall performance. The procedure has also been validated on the COVID-SC dataset under different scenarios, with accuracies ranging from 70.81 to 87.40%. In conclusion, our proposal provides a good accuracy appropriate for the early detection of COVID-19.