Someone found my public IP, and I think is DDOSing me?

Super noob here, so I apologize for any confusing statements.

So pretty much I was livestreaming yesterday on Twitch.tv, and a guy came in the chat saying some pretty rude stuff, so naturally I banned him. Not too long after I had banned the first user, someone else came in and threatened to take my internet down unless I unbanned his friend. I obviously said no, but low and behold my internet goes down. SO, after it came back up I kept playing games and livestreaming for a little, and then within probably 30 minutes my internet goes back down. They pasted my public IP address in the twitch chat as well. Fast forward to today (1/10/17) there was someone in my Twitch chat that said "I heard that someone was going around ddosing small streamers, I really hope it doesn't happen to you." Internet goes down again. I called Comcast asking if there was something that I could do, but they couldn't help a whole lot. Are there any recommendations that anyone might have to help?

Again, I apologize if any of this is really confusing, so please feel free to ask whatever you need. I really appreciate any help.