The non-detection of neutrinos from the brightest gamma-ray burst (GRB), GRB 221009A at the IceCube neutrino observatory allows us to put constraints on GRB model parameters like the dissipation radius, the Lorentz factor, and the cosmic-ray loading factor. We model the neutrino spectra and discuss the resulting limits on allowed parameter spaces. We find that our results are strong enough to constrain proton acceleration near the photosphere. Our new limit from a single source, is comparable and hence complimentary to the IceCube stacking limit. We also discuss the prospects for quasi-thermal neutrinos from the subphotosphere region in the context of neutron decoupling and colliding neutron-loaded flows, where we find that the latter might lead to a few events at IceCube with dedicated searches. Such observations at next generation neutrino detectors like IceCube-Gen2 and KM3NeT are crucial and would provide important constraints and insights into understanding subphotospheric emissions from GRBs.