Yeah, at the end of my period I usually get brown discharge. I wouldn't worry too much.

I've experience that as well, However it was after I had sex for the first time. Is that a problem?

Not really. Sex can cause uterine contractions during pleasure and orgasm, and this can push out some old menstrual fluid.

How long do you think it will last?

It shouldn't last very long unless you were close to your period; then you may stop until that begins.