Quantum computers in the Noisy Intermediate- Scale Quantum (NISQ) era face significant challenges due to inherent noise and limited qubit coherence. Accurate fidelity evaluation of quantum states necessitates multiple repeated measurements to obtain statistical results. But determining the optimal number of measurements remains an open problem due to the dynamic, device-dependent nature of quantum noise. Existing approaches either assume prior knowledge of noise models or rely on historical circuit data, limiting their applicability in practical deployment scenarios. This paper presents AutoFid, an adaptive and noise-aware fidelity measurement framework that automatically determines the number of required tests based on circuit structure and hardware feedback. AutoFid models quantum circuits as Directed Acyclic Graphs and estimates structural complexity via random walks, enabling principled estimation of measurement effort. It further incorporates transpilation-aware features such as gate fidelity, depth inflation, and crosstalk to refine iteration budgets. During runtime, AutoFid dynamically samples fidelity results and employs an early stopping strategy based on confidence intervals to reduce redundant measurements while preserving statistical guarantees. We evaluate AutoFid on 18 quantum benchmarks executed on real IBMQ hardware platforms. Experimental results show that AutoFid reduces measurement costs by more than 50% compared to both fixed shot and learning based baselines, while consistently maintaining fidelity bias below 0.01. Additional analysis using classical software testing metrics and ablation studies demonstrate its effectiveness, robustness, and adaptability across a wide range of quantum workloads.