Not too bad on the switchbacks; not too steep, and they are short. You can stop at each turn and catch your breath. It might help to keep your focus on the trail in front of you and think of something other than your fear of heights. Stay close to the uphill side when passing other hikers.
If you have music to listen to, that will help keep your mind on the task. Talk to your son and reassure him, taking the focus off our own nervousness. If you feel intimidated by certain sections of any trail, take a deep breath and move quickly through it.
The hike is worth the effort and you will feel a strong sense of accomplishment that will help you overcome other issues.
Here is something that gives a pretty good look at the trail:
http://www.modernhiker.com/2010/09/20/hiking-mount-whitney/