That's a tough one.. since his bottom is so sensitive, how about you put him in a bucket/pan of water to soak his bottom instead of full on bath?
If he was that plugged up, his glands and other parts are probably swollen too. You might need to apply some ointment. Just to be on the safe side, I think you should take him to the vet. Make sure there weren't any damange.
The thing about mistakes like this is that you'll ALWAYS remember and not do it twice.
I'm glad you found the problem before it caused more harm.