So here are my problems:

#1) I had sex about a month ago (we used a condom), the very next day I started my period.
But now, a month later, I'm a couple days late. I should have started on the 18th and I've had the cramps the past couple of days thinking i would start, but nothing yet. Should I be worried?

#2) I had sex (with the same guy) on saturday and the condom fell off. He says he's sure he pulled out in time, but he was still kinda freaked out. If i start my period today or tomorrow (that takes care of problem number 1) but should i still get the plan b just in case?

Pretty much my question is, if i have sex and i start within the next couple of days, should I be worried. Most of my friends, who have been sexually active alot longer than me, say no and that your period flushes everything out, but I'm still unsure.

I wouldn't worry about it. If you start your period, it means that you're not pregnant. Plus if you continue to worry about it, the stress could keep your period from coming longer, and that's just more worry for you.