Optical coherence tomography (OCT) is a popular modality in ophthalmology and is also used intravascularly. Our interest in this work is OCT in the context of airway abnormalities in infants and children where the high resolution of OCT and the fact that it is radiation-free is important. The goal of airway OCT is to provide accurate estimates of airway geometry (in 2D and 3D) to assess airway abnormalities such as subglottic stenosis. We propose $\texttt{NeuralOCT}$, a learning-based approach to process airway OCT images. Specifically, $\texttt{NeuralOCT}$ extracts 3D geometries from OCT scans by robustly bridging two steps: point cloud extraction via 2D segmentation and 3D reconstruction from point clouds via neural fields. Our experiments show that $\texttt{NeuralOCT}$ produces accurate and robust 3D airway reconstructions with an average A-line error smaller than 70 micrometer. Our code will cbe available on GitHub.