We present a detailed photoluminescence study of a (6,5) enriched DNA-wrapped single wall carbon nanotube (DNA-CNT) solid sample and an as-produced DNA-CNT solution. Multiple strong PL peaks were observed at excitation energies that do not correspond to the interband electronic transitions that are strongly enhanced by electronic van Hove singularities. These strong PL peaks are assigned to different mechanisms of excitation and relaxation, including one phonon, two phonon, hot luminescence processes, as well as radiative and non-radiative energy transferring mechanisms between neighboring nanotubes. These processes are assigned to different channels of phonon-assisted electron relaxation. The study shows that the electronic relaxation processes observed in PL can be used as a means to probe different physical interactions between photons, electrons, and phonons that are not separately identified in bulk semiconducting materials.