I took plan, had a normal period and now month later i am having brown spotting discharge for over a week. is this normal?

Few possibilities...: 1. Yes this can be normal and can cause irregular menstrual bleeding for up to a few months in dome cases. 2. You may have acquired a sexually transmitted infection, if you don't know your partner well, consider getting tested 3. Plan B only covers you if taken in time and only for that particular encounter, other unprotected sex could result in pregnancy. I suggest getting checked for STDs and BC