Nothing wrong with keeping your damaged ends if you're not ready to part with them yet. I recommend trimming them out gradually, even still. Personally, I'd ditch the unhealthy hair just because I don't like the look or feel of damaged hair on any part of my head.
Either way, once your damaged ends are gone and all of your hair is healthy and curly, I hope you'll come to really enjoy it! I bet it will look great with a little pampering