Accurate channel estimation remains challenging in high-mobility wireless systems because Doppler shifts induce severe inter-carrier interference (ICI) in Orthogonal Frequency Division Multiplexing (OFDM). We propose an unsupervised online channel estimation framework based on Implicit Neural Representation (INR). Unlike discrete-grid estimators, the proposed method decouples channel representation from the OFDM sampling resolution by modeling the time-varying frequency-selective channel as a continuous function of time-frequency coordinates. A Sinusoidal Representation Network (SIREN) with Gaussian Fourier feature mapping captures fine-grained channel variations and high-frequency details without offline pre-training or labeled data. For each received slot, the network parameters are updated by per-slot online fitting that minimizes a physics-aware ICI loss, while a confidence-aware decision-directed loop balances reliable pilots and dynamically harvested pseudo-pilots. Simulations in realistic Vehicle-to-Everything (V2X) environments show that the proposed method achieves near-optimal link-level reliability, significantly outperforming Least Squares (LS) and robust Linear Minimum Mean Square Error (LMMSE) estimators. Compared with supervised deep learning baselines, it also exhibits strong out-of-distribution (OOD) robustness under environmental distribution shifts, establishing an adaptable data-efficient physical-layer paradigm.