Laurie, you can paint it with the same kind of paint used for boats but you will have to strip it and repaint every couple of years, as is done with boats that are wet continuously or close to it.
A fiberglass section, shower wall or boat, is made in a mold and the first application is the color. This is called a gel coat and the actual fiberglass goes over that to be the inside of the panel. You can buy gel coat, but it is very difficult to apply and it takes air spraying equipment.
The next kind of paint to consider is a true 2-part epoxy paint. This will be your best choice if you have to paint. Go to an auto paint store or a boat store for this.
Some places have what they call "epoxy paint" but this is really just paint that can be used on epoxy. A one part paint will not hold up well.