Hello, Brown discharge after one week of unprotected sex is mostly suggestive of implantation bleeding. Here, you need to undergo one blood test for beta hcg and TVS scan to rule out possible conception. Early home pregnancy test is less significant. Other reasons are old endometrial tissue, pelvic or vaginal infection, hormonal imbalance, stress etc. Kindly, consult with your gynecologist after undergoing above test reports for further management. Maintain genital hygiene and practice safe sex in future. Good luck.