Well-being is a dynamic construct that evolves over time and fluctuates within individuals, presenting challenges for accurate quantification. Reduced well-being is often linked to depression or anxiety disorders, which are characterised by biases in visual attention towards specific stimuli, such as human faces. This paper introduces a novel approach to AI-assisted screening of affective disorders by analysing visual attention scan paths using convolutional neural networks (CNNs). Data were collected from two studies examining (1) attentional tendencies in individuals diagnosed with major depression and (2) social anxiety. These data were processed using residual CNNs through images generated from eye-gaze patterns. Experimental results, obtained with ResNet architectures, demonstrated an average accuracy of 48% for a three-class system and 62% for a two-class system. Based on these exploratory findings, we propose that this method could be employed in rapid, ecological, and effective mental health screening systems to assess well-being through eye-tracking.