I think that there are so many other factors outside being an only child that might impact upon an individual's confidence, that it is impossible to see it in isolation. I have met lots of people who have siblings who are not confident and have admitted this to me. Similarly, I have come across only children who fall into both camps. I am an only child and am confident in most situations, I have a friend who isn't - but we are from different backgrounds.
Even so, as the parent of a dd who is also 13, it is something that I have always kept my eye on. I think it is because I have always wanted to make sure that she was as confident as possible - but I would have done the same if we had more children.
One of the strategies that I have followed since she was quite young, is to put her in slightly testing situations, where she would need to cope. For example, sending her on holiday play schemes where she didn't know anyone - this was also true of her secondary school. I also give her a reasonable amount of independence. For example today, she went into London with some friends and she was able to get them to different areas of interest based on previous trips with us.
Inevitably there have been situations that have been upsetting for both of us. For example, she was with a difficult group of girls at primary school and when I look back, I feel that I should have intervened more.
I think that you can help her take care of her state of mind, just by talking about situations. I often do this, even if my dd doesn't want to listen! Unless a situation has got out of hand, I don't think that you can fix things, as they are beyond the age when this works. If you think about it, you won't be able to do this when she leaves home, so it is probably best to step back now. Although this is difficult, just think that with every negative experience that she takes on now, she will be far more ready to deal with something similar when she is older.