If we define ourselves by our experiences?

This doesn't really apply to me as I don't think I solely define myself by my experiences, not does my interpretation of them change uncontrollably. It may change slowly over many years and then I do have to re-evaluate various attributes such as how I was perceived, how I now perceive myself, why I acted the way I did, what I learned about myself and about others.

However, to answer your question properly (because you did start with an "if"), "if" this happened to me, I'd feel as if I was in a very uncertain and confusing world, that contentment (or anything other than fleeting joy) is impossible and, as an atheist, I probably would see the dissociation of death as the return to a natural state where my atoms play to the biochemical tune of some other life (or non-life). To quote Nabokov: the cradle rocks above an abyss, and common sense tells us that our existence is but a brief crack of light between two eternities of darkness.

I would add that this "crack of light" (or life) is a roiling uncertain avalanche of emotion and that life, for all its wonder, is very difficult for many people.