Overcoming fear in writing
Not all fear is bad - some fear will compromise your writing, but some will actually make it better.
There are two kinds of fear that a writer has to negotiate. Those fears that everyone has to deal with: fear of being alone, of never finding love again, of wasting your life in a job that's slowly killing you. Fear of never seeing your loved ones again, of losing your career, your partner, your house; of being attacked or abused, of the unknown, of dying. The fear of coming to the end of it all without having achieved what you always meant to achieve.
These fears are good fears, these are the things that remind you of what it means to be human, that connect you to everybody else. For a writer, they are grist to the mill, fuel for the fire. We all love a fluffy story and a happy ending, but for a story to resonate, to touch upon universal elements important to all of us, the writer needs to know his fears, to have spent time with the coward within - not only will he come closer to himself, but to the whole human race.
But there are also bad fears - the fears that will stop you writing freely and fluently, fears that may even stop you writing completely - but even these you can turn to your advantage.
Fear of being a bad writer
I don't believe there's a writer in the world who hasn't had this thought at one time or another. This is a very reasonable fear, and it's very possible that you are in fact a bad writer. Even the best writers in the world will write something appalling now and again - Hemingway said that the first draft was always shit, so you're in good company.
The fact is, it's quite alright to be bad. If you can recognise the fact that your work is bad you're already half-way to being a great writer - it's only by recognising the bad that you can start to make it good.
And even if you are a universally appalling writer, that can be fixed - by practice and learning. If you want it enough, you can get it. Check out this post for some ideas of where to start.
The thing is, you have to allow yourself the space to be bad, otherwise you're in danger of never writing anything at all.
Fear of criticism
This is a very real and understandable fear, and for me personally, was a turning point in my journey as a writer - the ability to invite and deal with criticism. There are generally a number of ways of dealing with it - ranging from heart-break and self-doubt to slavishly addressing every comment made about your work - clearly the correct response lies somewhere in between.
Even if you don't respond to criticism at all, you have to learn to deal with it, and I would suggest you learn that as soon as you can. It will feel like a baptism of fire, but you will be a better and stronger writer for it. It's best to learn how to take it from those you invite to read your work, or from fellow writers now, because if it ever gets published, absolutely anybody can say what they like about it, and worse, print or publish that opinion so anybody else can read it!
Fear of what people close to you will think
For a novice writer, this can be a real hurdle to get over when starting out. What will my mother think about my Oedipal theme? What will my partner think when she realises I've been imagining sex scenes like this? What will my parish priest think about the black mass in chapter 12?
Pick your own complex, but the reality is, if your writing with these constraints, you're never going to be a good writer. The only constraints you should apply are those demanded by technical considerations - pace, story, character etc.
You may elect to avoid certain subject matter due to you own personal taste - this is acceptable - but don't do it because your worried about what your mum might say. Chances are she's read, thought, or done much worse anyway.