Cryptology, a crucial discipline for safeguarding sensitive information against unauthorized access, underpins the Session Key Agreement Protocol (SKAP), which facilitates authorized access. SKAP generates unique cryptographic session keys for each session, allowing authorized users to access, share, and modify encrypted data. The current research landscape is dominated by the development of Key Agreement Protocols (KAPs) and key exchange mechanisms that are robust against known attacks and provide security to the cryptographic key. These novel KAPs leverage complex mathematical algorithms for enhanced security. This article introduces an innovative SKAP that employs Affine Transformation over Multivariate polynomials. The noncommutative and invertible nature of Affine Transformation forms the cornerstone of this protocol. The use of Multivariate polynomials augments the quantity of potential private keys, thereby amplifying security. The proposed protocol's security features are thoroughly analyzed and compared with existing key exchange mechanisms and SKAPs. Moreover, the paper encapsulates the application of the proposed SKAP in the realm of Telemedicine. This approach demonstrates the real-world implications and practical utility of this advanced SKAP.