For us, just being in the bathroom with the door closed wasn't enough. Being just outside the shower with the shower door open didn't work either. I needed to actually stand in the shower with the kids.
As Kathryn mentioned, obviously you can't subject either them or yourself to scalding water, but I would stand there with the water hitting my back, my little one with her head on my shoulder (not in the path of the water, of course)...exhausted. Eventually she would stop coughing, fall asleep, and with Daddy's help, I could transition the both of us to the rocking chair for the night. Lying flat aggravated the situation, so we slept sitting up.
A nice warm bath is a good idea too, Rapid.
My 10 y/o still does that sometimes.
Hang in there! Once they get older, you'll be able to use heavy-hitters like prescription cough medicine. Now we have a whole cold/flu routine that includes Rx cough medicine and inhalers, and it works beautifully. No more hacking up half a lung and sleepless nights.