Fear is one of those things that can freeze you up or free you up. It's a natural, instinctive act - given the caveman days, it's what kept us alive and drove us into acts of invention. Fear of the dark led us to create fire, for example. To create weapons to protect ourselves from the predators. To take up animal husbandry or farming against starvation. To form family groups to keep from being alone.
Obviously, the single mitigating factor is fear of death - necessity compels us survive, so ancient man adapted and moved on.
These days most of us aren't afraid of being dragged away from the campfire by a saber-toothed tiger, but the instinct of fear still drives us along...it's just been internalized for the most part. (Often in the form of phobias.)
Sure, there's always going to be things we're afraid of - spiders, car accidents, the dark, being lonely - and part of that still stems from that caveman brain. Instinct is a powerful motivator - but realistically speaking, with so much of modern life making things easy for us, it's hard to really put a finger on WHY one might be afraid of spiders these days. Sometimes it just can't be helped though. I was a complete introvert for quite a while - it was a massive triumph just to be able to pump my own gas at one point. Or buy a gallon of milk at the 7-11. I still hate cold-calling people - so the internet has been both bane and balm to my own growth in this respect.
With our physical bodies no longer being utilized for the harder functions of primary survival, we're left with turning much of our fears toward our inner selves. Fear of failure. Fear of success. Of not being pretty enough. Not being popular enough. Not being rich enough. Or good enough. Or fertile enough. Or whatever bit of irrationality the airbrushed mainstream consumerisms tells us we should be. (And that so many of us spend so much money and time on things that are either unimportant or really cannot be changed speaks volumes of our society and where our priorities lie.)
In some cases, fear is actually a good thing. It keeps us on our toes. After all - from an author standpoint, getting published is the initial goal...but once you're there, then what? You can't just sit there and rest on that single point of success. You have to keep writing, keep putting yourself out there, keep *growing* as a writer. (The danger point is when authors/artists/creative types start believing their own press, I think. It's easy to rest on your creative laurels if you're being lauded, but that 15 minutes is only going to last so long.)
But like everything else, the level and type of fear changes. It's no longer "What happens if I never get published?" but more along the lines of "What if people hate it? What if I can't do it again? What if my publisher drops me?" Lots of what-ifs there...but I think you have to figure out if what you're afraid of is something you can actually control.
If it's not, you have to let it go. I can't control if people like my writing, for example...what good does it do me to worry about that? But I *can* control my own writing - as long as I know I've done the best I can personally do and I'm happy with it, then that's all I can ask of myself.