You could try measuring the IR using a high reference resolution spectrum and see how it compares with you MILES IR.(Unless I am working low to the horizon or at the blue end just use a bright star like Vega, Altair, Regulus for example which can be recorded quickly.) If it is significantly different, it might be safer to just rectify the spectra you have already taken. (You can still submit them the BeSS setting the appropriate flag in the fits header.
To be a bit controversial (and this is just my personal view) I think for relative flux calibrated H alpha spectra, most of the time IR correction of a narrow wavelength range at high resolution is a waste of good observing time. (And may even lead to increased variability, though I need to quantify this). If you use a flat, You are already getting rid of all instrument affects as they divide out, leaving the flat lamp spectrum and the atmospheric extinction which hardly varies across the range. If you are using ISIS, this even removes the small slope due to flat lamp spectrum, assuming a black body at 2750K I believe so the IR ends up being effectively a horizontal flat line. In the projects I have been involved in where narrow range spectra have been used, the first step in analysing the data has been to rectify all the spectra first in any case.