Is it normal to get your period 8 days after you already had it if you are 15?

It could be. Maybe what you thought your period was just spotting before the actual period. That can happen. If you have just started puberty it takes a year or two before your cycle settles down to a regular cycle. This could be happening with you since you are 15. I will warn you the same thing happens when menopause starts when you are older. No one warns you about these things. I suggest you keep a calendar of your period and see if you see a pattern developing.