Firstly we want to say that it's normal to get scared when climbing. The fear of falling is inherently natural and most people have it. It's a good thing, as long as you learn to control it, rather than it control you.
Alex Puccio has suffered two pretty bad knee injuries from climbing. Once in isolation in a World Cup (ACL rupture, MCL, PCL, LCL and Meniscus tears) and another from dropping (in control) from the top of a boulder again, fully rupturing the ACL as well as tearing everything else.
As a result, dynamic movement and falling has created some obvious fears, that left alone would stop her from trying anything too high.
However, there are steps to help overcoming this.
1. Accept that you are scared. Let yourself know it and let those you're climbing with know it. If they aren't respective of this, they're probably not great to climb with.
2. Make sure the controllable aspects are in your favour: pads are perfect with no gaps and bends. Your spotter(s) is confident and with you the whole way.
3. Address the fear progressively. Take progressive falls, with assistance and spots to soften the landing. Learn how to land and where you'll land. Build the height of the fall (progressively) and learn that you are OK when doing so. Make sure you talk to your spotters (and vice versa) if it helps.
Reassurance is a good thing.
Be brave and push yourself. Commit more, use more power take slightly higher and progressive falls until you are either committing to the move fully and falling (learning that it is OK) or completing the move.
4. When you are confident, start making attempts from the bottom (start) and accept that on the go, feeling more tired etc, you may go back a step (mentally) and have to build up again.
This is normal.

Be safe, have fun, try hard and learn from your attempts.