This paper presents a new approach for effective segmentation of images that can be integrated into any model and methodology; the paradigm that we choose is classification of medical images (3-D chest CT scans) for Covid-19 detection. Our approach includes a combination of vision-language models that segment the CT scans, which are then fed to a deep neural architecture, named RACNet, for Covid-19 detection. In particular, a novel framework, named SAM2CLIP2SAM, is introduced for segmentation that leverages the strengths of both Segment Anything Model (SAM) and Contrastive Language-Image Pre-Training (CLIP) to accurately segment the right and left lungs in CT scans, subsequently feeding these segmented outputs into RACNet for classification of COVID-19 and non-COVID-19 cases. At first, SAM produces multiple part-based segmentation masks for each slice in the CT scan; then CLIP selects only the masks that are associated with the regions of interest (ROIs), i.e., the right and left lungs; finally SAM is given these ROIs as prompts and generates the final segmentation mask for the lungs. Experiments are presented across two Covid-19 annotated databases which illustrate the improved performance obtained when our method has been used for segmentation of the CT scans.