Should I try working at a higher intensity than is shown in the videos when I am having a good day (should I push myself more than what feels good)? 

Never push yourself to a point where you feel exhausted or in pain! If you are having a good day it is safe to increase your intensity a little bit and see how you feel, but do not overdo it because, most likely you will feel worse for the next few days afterwards. Challenge yourself but don’t go overboard.