Yes, you really can get pregnant after your period. Here's why -
If you have unprotected sex after your period, the sperm from that can live up to five whole days before completely dying off. If you ovulate a bit earlier in your cycle than expected, then it's quite possible for one of those late-in-the game sperm to find their way to the egg.
Here's a simple way to look at it:
The first day of your period is called Cycle Day 1 (or CD1).
Hypothetically, let's say your period lasts for five days and you have sex the next day. You had sex on Cycle Day 6. Then again on Cycle Day 7 and Cycle Day 8.
Now, let's say that you usually ovulate on Cycle Day 14 - two weeks after you started your last period but this month your ovulation came just two days early and you ovulated on Cycle Day 12 instead.
From Cycle Day 8 to Cycle Day 12 is four days. Four days that a few sperm from that last time you had sex could still be hanging out, waiting for their egg.
This is how, sometimes, you can get pregnant right after your period.
My advice is to wait to take a pregnancy test until you're four days away from starting your period. Begin testing that day (with an early result test) to confirm if your symptoms are pregnancy related or just pre-period stuff.