I used to suffer from that overanalysing of situations too, always delving in worst-case scenarios. So I decided to do something about it and started myself into zen buddhism.
Meditation has really helped me in that department, I'm now happier, anxiety is basically gone, and live better now.
If you haven't heard about this book, let me recommend it to you: Zen Mind, Beginner's Mind - Shunryu Suzuki (this is how I entered myself into this buddhism thing).
I'd like to second your opinion -- meditation has helped me tremendously in many ways, especially in, broadly speaking "getting me out of my own way".
I'd suggest starting with the book "Mindfulness in Plain English", available from free online. Another good book, available online, is "Mastering the Core Teachings of the Buddha".
Also, try some audio talks from Jack Cornfield, Pema Chodron, Gil Frondal, Shinzen Young, or whoever seems to work for you. Listen to them when you go on a drive more than half an hour. But the important thing is to put in some time meditating.
Meditation has really helped me in that department, I'm now happier, anxiety is basically gone, and live better now.
If you haven't heard about this book, let me recommend it to you: Zen Mind, Beginner's Mind - Shunryu Suzuki (this is how I entered myself into this buddhism thing).