I was hacked!
A couple days ago, I had a couple friends on Twitter send me a direct message asking why I sent them a weird message. I didn't know what they were talking about. Apparently, my account had been hacked. The day before, I received a message from a friend, asking me to go check a quiz out on this link. It was a vague message, but since it was from a friend, I clicked the link. Twitter asked me to log in, so I did. That's when they got me.
This "login" request was a fraud. With it, I gave them my name and password. They used this to send messages of the same kind to all of my followers. If this has happened to you, I can tell you how to fix the problem.
You need to immediately change your Twitter password. Once you've done that, they will not have access any longer. If your friends tell you they received strange message, give them this same advice. I believe this should be the end of the problem.
If anyone has any other information on how to protect yourself on Twitter, please share in the comments.