We have recently demonstrated efficient high power CW laser operation in Er doped Y2O3 at cryogenic temperature. The selection of laser host was based on the low-phonon nature of Y2O3, where the I-4(11/2) -> I-4(13/2) transition is highly radiative. Further increases in mid-IR power scaling and efficiency require in-depth study and analysis of basic spectroscopic properties of the I-4(11/2) -> I-4(13/2) laser transition, such as laser emission cross-sections, fluorescence quantum efficiency, fluorescence branching ratios and inter-ionic interactions in a wide dopant-concentration and temperature range. In this work, we report the results of experimental measurements of quantum efficiency and branching ratio of the erbium initial laser state of I-4(11/2) in Y2O3 ceramic at the temperature range of 10 - 300 K. A series of Er:Y2O3 samples with dopant concentration between 0.2-10 at.% were used for fluorescence and absorption measurements. The fluorescence from the energy states corresponding to the visible, IR, and mid-IR transitions were studied under short-pulsed diode laser excitation. Spectrally-narrowed fiber-coupled semiconductor laser modules emitting at similar to 808, 980, and 1530 nm with variable power density were used for fluorescence excitation of three different Er states. The energy transfer processes for both down-and up-conversion, affecting the Er: Y2O3 mid-IR laser operation, were analyzed. A comparison between the experimental and simulation results are presented as well.