Is there any way to save hair burned by a hair iron?

The lower back part of my hair got burned by a curling iron and is all frizzy. Is there any way to fix this other than cutting it off?

It wasn't this bad at first... Only the ends were bad, while the roots looked fine, so I just left it alone. But one day, I noticed that even near the roots, my hair had turned rough and frizzy like pig bristles. I've tried applying a hair pack only to the frizzy parts and leaving it on for a long time, but it doesn't seem to work.

Is it true that the only solution for burnt hair is to cut it off? If I cut it, will straight, soft hair actually grow back?