Pinkish brown discharge day after rough sex... no condom.. we used baby oil as lubricant also. what could this be?

Likely vaginal traum: Likely coming from vaginal trauma. Not to worry you but chlamydia can cause "post coital" bleeding as well. It's likely vaginal, however, just get checked out if it keeps happenning or you get low abdominal pain. Good luck.

Could be irritation : Of the vagina or cervix, or other, baby oil not recommended, astroglide or replens moisterizer much better, your gyn can do an exam and determine the cause and rough sex often can cause problems, sex sholdl be enjoyable without making it rough, because next time something worse may happen like a vaginal tear or laceration or other and I have seen that before and had to take the pt to surgery.