If you have an open burn wound you should keep it covered with a medical dressing while showering or bathing to prevent water and other dirt etc from getting into the open burn wound.
If you do shower with an opened burn wound it could make it more painful or worse but as long as you keep the burn wound covered with a dressing then it should be okay to shower.
I once had an open burn wound on my leg and I covered it with a dressing while showering and it was never a problem.
The doctor advised me to keep the open burn wound covered when showering but I should also keep the area around the burn wound clean with some soap and water.