Yikes, those sprayer heads have a handle to turn them on to spray. Just like regular garden sprayer heads. And they only spray if you are letting water in (by flushing) while holding the sprayer head handle down. Is it possible the head is sitting where the handle is being pressed in and allowing water that way? Check that first.
Second, you might just want to go get another one. I had one on my last toilet. I recall it was attached to the hose just by a hose clamp. If yours has that, you can loosen the hose clamp, remove the sprayer head and put on another sprayer head and re-tighten. There’s probably another hose clamp where it connects at the back of the toilet to the hose. A new sprayer head might come with a hose in which case you might want to use that one instead of the older one.
Best of luck! Let me know how it goes.