Is a late cycle pregnancy?

my cycle was later and before that I was having very bad
discharge and all the issue of being pregant whats wrong

If you are sexually active, then yes, you could be pregnant. Most women do not get their period when they are pregnant, but some actually do. So the only way to know is to take a pregnancy test or visit your ob-gyn.

A late period could be due to make things other than pregnancy though, so it is usually nothing to worry about.