The self is the innermost sense of a person. The self would be considered akin to the soul. We debate a lack of this or that within reference to the self, so the existence, at least from a standpoint of consideration based on human personality, is clearly relevant. Low “self”-esteem. Lack of self-respect. Self-serving. Self-absorbed. These are all just a few of the many aspects of “self” that go about making up what or who a person is. So most assuredly the self does exist, even if in many different forms.
Granted, you could pitch some theory about how we're all hypothetical and may or may not actually exist. However, to keep it simple, I'll stick with Descartes: I think, therefore I am.
You could also argue that our thoughts and actions are simply the result of chemical interactions, but that doesn't explain why identical twins show different personalities at early ages. The brain has an effect on our behavior, certainly, but there is something else - mind, spirit, self, whatever you want to call it - that steers and can override the brain.
Anything can exist as long as people have faith and believe in it. Many things in our life and in our time can not be proven, or touched, but that does not mean it is not there. Sometimes you just have to have faith and believe that despite all odds, anything can be possible.
Intangible concepts like the "self" don't exist in a strict sense but can exist as they can be useful concepts. But if you find that "self" does you no good then you should not be feel compelled to use the concept or give it any currency. As its somewhat of a fluid concept that depends in part on what "self" means to you.