If it continues longer than that, you can always talk to school nurse, or maybe some kind of health specialist. Don't worry! A lot of other women goes through the exact same thing.
Yes, it is normal. For me, the longest it took for my body to completely rid of the brown discharge was nearly a month! Depends on how you're feeling that month.
That's actually pretty normal near the end of the period. I always get them near the end. It's the body telling you that you're nearing the end of the period and the older blood turns brown. If you google about it, you'll learn all the details.