I've often used a little toilet shower, but it didnt make any big difference to me. It was soothing though to let the water run while the butt-pee was expelled, as the mix of the two waters would result in a less acid liquid.
I am quite sure it is hydrocloric acid, so if you have a lot of burn, the thing to do in my experience is take less ES. People have very different conditions in the bowels, mine are clear very early and when that happens the hydrochloric acid passes through. Not a nice thing. In the last 2 flushes i reduced the ES and the burn was gone.