To "look oneself" can be used in a sentence like "When I do something bad, afterwards, I cannot look myself in the eye." In this case, I mean that I find it difficult to look into my own eyes, say in a mirror, if I have a guilty conscience.
Another way of using "look oneself", according to the Oxford Dictionary, is: to look oneself, is to appear one’s normal, healthy self> Example: "He just didn’t look himself at all". This is a different use. If I don't "look myself", it means I look sick or different from my normal self in some way.