Longitudinal analysis of optical coherence tomography data is crucial for monitoring retinal disease progression. In such diseases, pathological fluid accumulations may vary considerably between examinations, causing substantial alterations in local tissue morphology. These non-correspondences challenge classical image registration methods, while convolutional registration networks typically require large datasets for training. To address this gap, we introduce FRINR, a fluid-aware registration framework based on implicit neural representations. FRINR performs pairwise registration by jointly estimating a deformation field and a residual image: the deformation aligns anatomical structures shared across time points, whereas the residual disentangles pathological changes such as newly formed fluids, guided by a sparsity constraint. In this way, FRINR enables fluid-aware registration of severely altered retinae while maintaining plausible deformation fields. Moreover, the residual images allow unsupervised detection of new pathologies without large datasets or expert annotations.