As far as I'm aware you don't take continual health damage when you choose to soul trap yourself to enter the cairne. Instead you take a reduction to your base health stat, which will persist until you find your soul stone.
That you're taking continual damage is odd, and I'd say a glitch. As to how to fix it? No idea. You could go back to a save just before you entered and re-run it, but that's the best I have. Sorry
