Sex at the end of my period: pregnancy chances?

You don't say how long your cycle is, so I will base my answer on a typical 28 day cycle.

Day one is the first day of bleeding.
Typically a period lasts for 5-7 days.
Ovulation typically occurs around 14 days before your next period.
Once released at ovulation an egg is viable for about 36 hours.
Sperm can live inside the fertile female for upto 5 days.

So your window of "high fertility" is from 5 days before ovulation until the day after ovulation.

So for a typical 28 day cycle you would likely have a high fertility window of day 9 - day 15.

However, every woman is different and some ovulate early, or even whilst still menstruating, some ovulate late.

The only way to know for sure if you are pregnant is to take a pregnancy test if you miss your next period.

In the mean time always use condoms, any time you have sex.
Also make an appointment with your doctor, if you are pregnant you will need to arrange pre-natal care and discuss your options. If you are not pregnant, you need to arrange some form of birth control to prevent scares like this in the future.