A week after ovulation and white discharge has appeared as well as cramps similar to period pain. is this a sign of successful conception?

Not symptoms : White discharge and cramping are so common and are nonspecific findings to any particular problem. Neither of these would lead me to thinking that someone has conceived. A much better approach would be to simply take a pregnancy test 7 to 10 days after intercourse. This will give you a reliable answer.

No: Don't the cause of your cramping but it is not classic for conception.