Is the brownish discharge that preceded menstruation by one day, and was accompanied by a pain different from the usual menstrual pain, considered menstruation that necessitates re-performing the prayer that was offered after its appearance?

This brownish discharge is not considered menstruation as long as it occurs outside the usual period. What was obligatory upon you was to perform istinja' (washing private parts), wudu' (ablution), and offer the prayer. If you did that, then you are not required to repeat any of the prayers.