A good vibrato is something that is smooth and pleasing to the ear. If the vibrato is tense or shaky sounding then that is most likely what is causing the suffering in your hand and arm. A good practice for vibrato is to position your bar over a fret and play a note or chord.  Then, after the note(s) start sounding, slowly roll the bar just in front of the fret and just behind the fret.  What you are creating is a smooth roll of the bar on the strings.

The bar should not slide on the strings. And however much you roll the bar in front of the fret, that's how much you should roll the bar behind the fret for perfect intonation. The hand, wrist, and arm move together to roll the bar. So just like a singer, sing the note first, then slowly bring the vibrato in for the effect and texture of the note.  This should always sound like smooth waves and never shaky or jittery.