I'm on birthcontrol. had sex week and a day ago. have had a brown discharge for three days. what's going on?

Breakthrough bleed: Breakthrough bleeding (bleeding at the wrong time) is very normal on birth control. It happens in about 1/3 of users. Its no big deal and usually self corrects over time. If you are not satisfied or it continues to happen then consider using a different birth control method. It is a common side effect and does not mean something is wrong or that the pill is not working.

Spotting? STD? : If this is a new partner or if you didn't use a condom, please go get tested for an STD. And if you missed any birth control pills, that can cause withdrawal bleeding or what you're calling brown spotting.

Get examined, tested: What kind of birth control? If you are on a progesterone-only based treatment, spotting is not unheard of. Did you use a barrier (condom) or were you exposed to to skin & semen? If you are young, you may have a vulnerable "transformation zone" but one would expect bleeding sooner after the trauma. You may have a cervicitis from an infection, a cervical polyp or Nabothian cyst. Get a speculum exam.