The rapid shift towards digitalization of medical data has introduced an urgent requirement for strong and secure methodologies that preserve the confidentiality and integrity of sensitive medical images. This paper proposes an effective and secure scheme for the encryption of medical images, which combines Reversible Data Hiding, Integer Wavelet Transform (IWT) and a Chaotic encryption process involving novel chaotic maps. The proposed technique first applies a 2D IWT to decompose the input grayscale medical image, resulting in four sub-bands, namely LL, LH, HL and HH, which facilitates a selective and effective encryption process. Further, a chaos-based cryptographic algorithm is deployed to encrypt the high-frequency sub-bands, which reduces the computational cost significantly while ensuring the visual security. Additionally, RDH is deployed for embedding metadata or patient-related information in the encrypted image, which guarantees lossless recovery. The methodology is validated via parameters like entropy, correlation, and computational time, thus proving its suitability for secure telemedicine applications where data protection and reversibility are of critical concern.