Image encryption has attracted much interest as a robust security solution for preventing unauthorized access to critical image data. Medical picture encryption is a crucial step in many cloud-based and healthcare applications. In this study, a strong cryptosystem based on a 2D chaotic map and Jigsaw transformation is presented for the encryption of medical photos in private Internet of Medical Things (IoMT) and cloud storage. A disorganized three-dimensional map is the foundation of the proposed cipher. The dispersion of pixel values and the permutation of their places in this map are accomplished using a nonlinear encoding process. The suggested cryptosystem enhances the security of the delivered medical images by performing many operations. To validate the efficiency of the recommended cryptosystem, various medical image kinds are used, each with its unique characteristics. Several measures are used to evaluate the proposed cryptosystem, which all support its robust security. The simulation results confirm the supplied cryptosystem's secrecy. Furthermore, it provides strong robustness and suggested protection standards for cloud service applications, healthcare, and IoMT. It is seen that the proposed 3D chaotic cryptosystem obtains an average entropy of 7.9998, which is near its most excellent value of 8, and a typical NPCR value of 99.62%, which is also near its extreme value of 99.60%. Moreover, the recommended cryptosystem outperforms conventional security systems across the test assessment criteria.