Can a woman get pregnant the next day after her period ends without having sex just a slight contact of the sperm with her vagina ?

No risk, but...: Conception is very unlikely immediately after menstruation, also very unlikely without ejaculation in the vagina. There is no realistic chance of pregnancy from this event. However, you seem to be on the verge of being truly sexually active, i.e. having intercourse, even if not intended. Please get on birth control and have condoms handy for STD protection (even if difficult in your culture).

See below: If you miss your period by 4-5 days, do a home pregnancy test. If the result is negative repeat the test 4-5 days later unless you get a period by then. Use first morning urine and follow the instructions for the test carefully. If you do not wish to be pregnant, use contraception all the time, every time. You may consider implanted contraceptive, or IUD. Get HPV vaccine.