Very young (t \(\lesssim\) 10 Myrs) stars possess strong magnetic fields that channel ionized gas from the interiors of their circumstellar discs to the surface of the star. Upon impacting the stellar surface, the shocked gas recombines and emits hydrogen spectral lines. To characterize the density and temperature of the gas within these accretion streams, we measure equivalent widths of Brackett (Br) 11-20 emission lines detected in 1101 APOGEE spectra of 326 likely pre-main sequence accretors. For sources with multiple observations, we measure median epoch-to-epoch line strength variations of 10% in Br11 and 20% in Br20. We also fit the measured line ratios to predictions of radiative transfer models by Kwan & Fischer. We find characteristic best-fit electron densities of \(n_e\) = 10\(^{11} - 10^{12}\) cm\(^{-3}\), and excitation temperatures that are inversely correlated with electron density (from T\(\sim\)5000 K for \(n_e \sim 10^{12}\) cm\(^{-3}\), to T\(\sim\)12500 K at \(n_e \sim 10^{11}\) cm\(^{-3}\)). These physical parameters are in good agreement with predictions from modelling of accretion streams that account for the hydrodynamics and radiative transfer within the accretion stream. We also present a supplementary catalog of line measurements from 9733 spectra of 4255 Brackett emission line sources in the APOGEE DR17 dataset.