Recently, the advent of Internet of Medical Things (IoMT) has effectively alleviated the problem of difficulty in accessing medical services. However, during telemedicine, various medical images containing sensitive private information are exposed in communication channels. Therefore, there is an immediate need for an effective encryption method to ensure the secure transmission of medical images. In this paper, an image encryption algorithm is proposed based on a new chaotic model and an enhanced S-box. Furthermore, the proposed encryption algorithm is applied within a novel asymmetric image encryption framework. Firstly, to address the problems of narrow chaotic intervals and uneven trajectory distribution present in some existing chaotic maps, a two-dimensional cross-sine-modular model (2D-CSMM) is constructed. Secondly, in conjunction with the DNA algorithm, an enhanced S-box is proposed. Finally, in order to effectively protect key transmission as well as to enhance the system's resistance against chosen plaintext attacks, a novel asymmetric image encryption framework is designed by integrating the Elliptic Curve Diffie-Hellman (ECDH), Elliptic Curve Cryptography (ECC) and SHA-256 functions. And the secret key is computed from the cipher key, the shared key, and the native key associated with the plain image. Comprehensive experimental results demonstrate the high efficiency and the resilience of this new algorithm against common attacks.