Welcome! I like your name.
In response to your paradox:
It all depends on which theory of time travel you subscribe to for said paradox. There are three
main theories, and each one is vastly different in the way it works, and thus reacts differently with your paradox. I will briefly go over each theory, and explain it's relation to your paradox.
The first two theories are very similar. I, personally, like to call these the "loop theories," as everything that happens in the past affects the future that already exists.
The first of the loop theories is the fixed timeline. In the fixed timeline, in traveling to the past from the present, everything that you do has already happened. You are not changing anything, history already records your passage into the past before you actually do it. For example, if you travel back in time and kill your grandfather, you may seriously wound him, but not kill him. He would go to the hospital, and be in the same room as your grandmother. That would be where they meet, and they get happily married a few years later. In this case, you are the reason they got together in the first place, and they wouldn't have gotten together if you hadn't gone back in time in the first place.
The other loop theory is of the mutable timeline. In the mutable timeline, everything you do in the past can have a potentially catastrophic affect on the future. This is the most widely accepted theory, yet generates the most paradoxes. Your paradox stems mainly from the inconsistencies of this particular theory.
Separate from the loop theories, is the theory that I like to call the "branching time theory," commonly known as the multiverse theory. In the multiverse theory, alternate universes are created at the instant that a living being makes a decision. A new universe is created for each decision that is made, and they "branch off" from their original universe, with the "trunk" being the first universe, before living organisms ever existed. By this theory, there are billions to the billions to the billions of alternate realities, each one more and more different from the ones that came before. For example, there would be at least four different universes: one where I didn't click on this thread; one where I did, but chose not to respond; one where I chose to respond, but wrote only a few short phrases of welcoming; this one. By this theory, your paradox isn't really a paradox. It is completely possible as you can kill your grandparents, and while a future you won't exist in that timeline and any timelines that branch off of that one, the future you could potentially be in any of the others. It depends on the decisions that were made, but the possibility would be there.
It's really up to you which theory you wish to follow, and it is fun to consider how your paradox fits in each theory. Welcome to eGO, and I hope I didn't scare you off
tl;dr: I really like my philosophy, especially in relation to time 
Also, Yes and No, being a paradox that will always be the answer. If you go back and stop yourself you'll make it to where you weren't born to stop yourself and it will be a loop of you stopping yourself from stopping yourself. And then Reapers will come and eat everything.
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