If I had intercourse and he ejaculated in me two or three times, but I started my period the next day. Could I be pregnant?

While it is very very unlikely, there is a small chance that you could be. Even sex during the period has lead to pregnancy in a few cases.

Remember sex can cause pregnancy, the when just lowers or raises the odds of it happening.
If you are going to have sex, remember no birth control is 100 percent and no time of month is 100 percent. It just reduces the odds.

So it is not if, but what are the chances each time you have sex. That is why only those people who are ready to have a child should be doing it at all without some protection, and those others should know that it still can happen

How old are you and he? If he's going unprotected then he is being selfish and your risking pregnancy. Is this the person you want to be stuck with for the rest of your life?

Although you started your period, there is still a possibility you could get pregnant. Sperm does not just disappear just because the women's cycle took place. Semen can stay in the vagina for up to 7 days.