6G networks are booming, and they will transform healthcare; ultra-low latency, massive connections, and intelligent services will finally reach critical applications. Real-time performance, standardization, and scalability of healthcare networks are impacted by having various categories of devices, changing workloads, and changing resource requirements. This paper suggests a new AI-based method for standardized 6G healthcare systems, referred to as the Cognitive Autonomous Resource and Edge Collaboration Framework (CARE-6G). The use of cognitive AI agents together with edge-cloud cooperation in CARE-6G enables automated prediction, allocation, and optimization of computing, storage, and networking resources. The framework is constructed hierarchically such that edge nodes perform low-latency processing, while cloud infrastructure performs big-scale analytics. AI-based predictive orchestration ensures that the needs for workloads and healthcare services can shift. The experiments indicated that CARE-6G is 35% quicker, 30% more resource-efficient, and 27% more reliable than the existing practices. When compared to the best methods available, CARE-6G was 39% faster, 30% better at using resources, 27% more reliable, 25% less power-hungry, and 15% better at getting things done.