Yes. It can be done. The thing is that you have to talk yourself into the benefits and drawbacks of worrying. I was about 26 when I just let it go, maybe not as old as some, but still well set in my ways. In fact, when I was 18 I remember my mother telling me to stop acting her age and start acting my own!
I came to a point where I was waking up in the middle of the night with my heartrate at about 130. My normal heart rate is about 60, and when I woke up, I had been sleeping/resting. At some point, I came to realize that I could live life now and here instead of dealing with all my perceived problems years in advance. Every time I would start to worry, I would make myself remember that I could be happy until something bad happened, and that a life of worry wasn't a good life. Trauma could wait until it was called for. Sure, I still worry. But, when my family calls me, I don't automatically assume that somebody died. It has worked well for me, but honestly I couldn't go on the way I was living. I worried about everything, and had to go through some pretty dire straights to have this pounded into my thick skull. If you think that the worry is overcoming your life, write a plan of action. When I start to worry, I take some deep breaths and remind myself to keep on top of the world until their is a problem. My story is pretty vague, but I am so much happier and relaxed now that I choose to live life now and here instead of despairing over possibilitis of problems. That despair only holds you back.