The Internet of Things (IoT) is a network of interconnected objects, which congregate and exchange gigantic amounts of data. Usually, predeployed embedded sensors sense this massive data. Soon, several applications of IoT are anticipated to exploit emerging 6G technology. Healthcare is one of them, where the 6G-inspired paradigm may facilitate the users to exchange information through hundreds of sensors under the assumption of Artificial Intelligence of Things (AIoT). Integration of medical sensors with AIoT is known as Artificial Intelligence of Medical Things (AIoMT). The secure and seamless interactions among 6G-enabled AIoMT users should be the primary challenge. Furthermore, resource-constrained wearable sensing devices, with their inability to execute complex security solutions, provide an ideal attraction for malicious entities to launch diverse attacks. These challenges have motivated us to design a cost-effective authenticated solution (CAS) for 6G-enabled AIoMT healthcare applications. Our CAS protocol not only prevents cyber threats like impersonation session key secrecy but it can also prevent physical threats like hardware tampering. We observe formal and informal security validations to endorse its robustness and effectiveness. Performance comparison reveals that the CAS protocol offers maximum security enrichment. Moreover, CAS is cost-effective as it has achieved 33% and 60% reduction in computation and communication overheads, respectively, compared to contemporary competing related protocols.