In quantum optics experiments, heralding, a form of conditional state preparation, is a useful tool for creating photon-number states from nonlinear optical sources for quantum-information science experiments. Heralding occurs when one photon from a correlated pair is detected to herald the presence of the other photon, labeled the signal photon. However, as heralding is extended to two or more photon pairs, the presence of noise photons in the herald channel quickly degrades the photon statistics of the signal photons. We create two-photon number states from a non-degenerate, third-order nonlinear optical fiber source with double heralding and present a method for verifying these photon-number states. The consequences of noisy heralding on the statistics of states created via third-order nonlinear processes are analyzed. We present a method for estimating the effects of noise photons on the signal photon statistics. Additionally, we prove the equivalence between noise in the herald channel and a loss in the signal channel. We utilize this equivalence to infer the photon statistics of the photon-number states in the signal channel that would be present in the absence of noise in the herald channel. By measuring the statistics of the signal channels with noise in the herald channel and comparing to the inferred, noise-free distribution, we can estimate the potential benefits of additional noise-reducing procedures on the experiment.