We had the same mishap our first winter. We know better now.
The shower head has metal end pieces, with a plastic handle in the middle; the plastic part had split and squirted water when under pressure (i.e. when the pump ran). The metal part wasn’t affected.
My fix was to remove the plastic component, then make up some epoxy glue (Araldite), and dribble it into (and around the inside the handle whilst it was still fluid. This re-lined the inner part of the handle with a new waterproof inner-skin
No more leaks 🙂