I had my period on the 2nd and I just had unprotected sex on the 19th is it possible to get pregnant?

Of course you can get pregnant. Unprotected sex is the way most humans make babies.

Any time there is penile insertion there is a risk of pregnancy.

Of course you can, even if you used 3 or more forms of birth control.

Any time you have sex, ANY TIME, even when you're on your period, pregnancy is possible.

So yes, pregnancy is very possible.

It appears it would be close to an average time when you would be fertile
It is possible.