To avoid rounding errors associated with the limited representation of significant digits when applying the floating-point Krawtchouk transform in image processing, we present an integer and reversible version of the Krawtchouk transform (IRKT). This proposed IRKT generates integer-valued coefficients within the Krawtchouk domain, seamlessly aligning with the integer representation commonly utilized in lossless image applications. Building upon the IRKT, we introduce a novel 3D reversible data hiding (RDH) algorithm designed for the secure storage and transmission of extensive medical data within the IoMT (Internet of Medical Things) sector. Through the utilization of the IRKT-based 3D RDH method, a substantial amount of additional data can be embedded into 3D carrier medical images without augmenting their original size or compromising information integrity upon data extraction. Extensive experimental evaluations substantiate the effectiveness of the proposed algorithm, particularly regarding its high embedding capacity, imperceptibility, and resilience against statistical attacks. The integration of this proposed algorithm into the IoMT sector furnishes enhanced security measures for the safeguarded storage and transmission of massive medical data, thereby addressing the limitations of conventional 2D RDH algorithms for medical images.