Can part of a tampon break off while in use? i used one last night before bed and woke up with no period until later that night. this is not normal.

Yes: Just about anything can break, although tampons normally don't. With that said, I suspect you want to know what to do next, right? 2 choices: check inside yourself - you can't lose anything inside your vagina b/c it's like a pouch. Or go to ER or see your Family Doc/GYN/Planned Parenthood for someone else to take a look see. Of note, irregular menses are common but so are STDs/STIs w/o condom use.