I was wondering does the bleeding after dose of morning after pill count as menstrual cycle?

Nope: It does not. Hormones are tricky, you know your body best, see how similar the bleeding is to past cycles.

It may or may not.: Potential Side effects w emergency contraception include menstrual flow changes (spotting, bleeding, early or late period). Take pregnancy test & notify Dr if your period is 7 or > days late. The bleeding may be be between cycle bleeding or there is potential for an early period.