How to prep jicama - is peeling necessary?
Jicama does have a tough thick skin that is usually always removed.  As you know from your experience there are two layers...the outer dark papery skin and then the tough dark yellow fibrous portion.

The best way I've found (with least amount of frustration) is to peel it the same as you would a pineapple:  Trim off both ends and then cutting from top to bottom following the countours of the vegetable to cut just under the skin. 

I've never seen or heard of anyone using it skin-on.