Hello.
So I got my period on the 13th of this month, until the 18th.
Iam on birth control and started a new pack on the 17th.
Had unprotected sex on the 18th...
My next period is on December 11.
Yesterday when whiping myself, a mucus appeared with a little bit of a reddish/brown. I have read that can be related to pregnancy, now I feel paranoid.
Can I be pregnant? Please help.

You can always get pregnant when you have sex, pills or not (very low odds on the pill), but the bit of mucus and blood do not mean you ARE pregnant.
It is very common to have a mid-cycle discharge, and this is what yours sounds like. From the 13th to the 29th is 16 days. That's 'middle' enough.
Try not to say when your next period is as though it's 100% truth - even on the pill, it can vary.

The word 'Mittelschmerz' is German for the symptoms of mid-cycle. Have fun reading!

If you're on birth control then you didn't have unprotected sex, unless you missed or skipped a pill. Is that what happened?

Discharge between cycles is very normal, and happens to all of us at one time or another. But, having said that, pregnancy is always a possibility, even with birth control, no form of birth control is 100% effective.

Wait until your next period is due. If you miss it, wait at least a week (2 is better) and then test using first morning urine. If that test is negative, wait and see what happens with your next period. If you miss it then take another test or see a doctor for a more accurate blood test.

Good luck.