Some racist people on YouTube are leaving me mean messages. My feelings are hurt now, even though I stopped replying to them

Delete the messages. You have the right to remove them. Also, report them for hate speech/harassment.

But I don’t know how to block and report them on YouTube on the iPhone

Use a desktop, then.

I agree with that. Report them!   Don’t let those message get  deep into your heart. These peoplke are not worth it. Be proud and keep your chin always up.

Hey hun! Don’t worry about the people who are harrassing you. They most likely don’t have a life if they’re picking on someone over the internet :p.

Just keep your head high and ignore them, and like McDonalds said, just block and delete their comments on a laptop or desktop computer.

I found this pertinent: http://www.karmatube.org/videos.php?id=5633