To compare your images, you will need to correct them radiometrically and also for atmospheric effects. The radiometric correction can be done in certain softwares which access the signal gain and offset data over the web and make the appropriate adjustments for you.
The atmospheric corrections are more difficult and require the isolation of the atmospheric spectrum and its removal by a dark-subtraction techinque. The atmospheric spectrum can be found in pixels over deep water. Finally, the normalisation process you refer to is still required to convert your data to pseudo-reflectance.
I am happy to correspond further should you need more help.