I have been using ear plugs, although for some reason I cannot insert the plug in the right ear decently. In the left it works perfect and I can quickly and safely insert it deep enough to block noise. The right ear somehow it's not working, and often the plug falls out. (any thoughts on this?)

The reason for noise cancelling earphone is: (a) above problem for me (b) ear plugs are an overkill in many situations (c) my neuro thinks that the more I forget about the concussion, and wear and do things that look and feel normal the better my chances...

I think (c) is a good point. For some wearing "ear plugs" is normal for others, they are self-conscious and prefer something cooler... I think whatever works for you...