I don't enjoy speed or heights. You have described it perfectly. I can peddle at speeds on the flat with no problem
It's not the speed that scares you, it's loss of direct control. You can't feel your pedals pushing you along and this makes a 9 year old girl out of you. (Similar to why so many people are scared of airplanes... control issues) Try some VERY light taps on the breaks and occasionally matching your cadence w/ your speed and hopefully your cerebral will be able to keep up.
If you still feel like peeing yourself... you should probably go ahead and do it. There's less shame in that than in being a cyclist who's afraid of hills.