The emergency contraceptive pill you took carries a high dose of hormone, and shifting your next period earlier or later than usual is a well known, expected effect of it, not a sign of a problem. The flow that cycle can also be lighter or heavier than normal.
Next Steps
Give it up to a week past your expected date before worrying. If your period still hasn't come by then, take a home
pregnancy test to rule that out.
Health Tips
See a gynaecologist if the delay crosses a week, or if you find yourself needing this pill often, since it isn't meant for regular use.