Until your an 0-4 or above and your disconnected from the "men" and knee deep in paper work. The best officers in my book were the ones who were enlisted first. They knew the men better than west point grads or ROTC types.
OP- This is a classic scenario of tattoo regret. Even if you don't know it. Now its holding you back from potential dreams. As said earlier, get it removed and go forward with the military. You will get out of it what you put in. I enjoyed it for the most part.