Any time there is penetration even if no ejaculation occurs there is a chance of pregnancy no matter what point in your cycle even if you are on your period. If you are not wanting to get pregnant you need to look into getting on a reliable form of birth control such as IUD, shot, patch or pill and ALSO use a condom every time. If you live in the US you can either go go your gyno, local health department or planned parenthood. Planned parenthood and the health department offer exams, pregnancy tests and birth control options at reduced cost or free
If your period just ended yesterday I really don't think you could get pregnant from having sex with him today, generally you ovulate 14 days after the start of your period.. if you have regular periods...If you aren't trying to get pregnant you should use a condom or take the birth control pill because trying to figure out when you are ovulating and not having sex at those times isn't a fool proof way to make sure you don't get pregnant :)