I was prescribed ferrous sulfate (325mg) on May 29th. For 2 weeks the middle of my bottom lip has been dark brown and chapped. Is this a side effect?

Unrelated. The two are likely to be unrelated. You may use an over the counter emollient like Chap-stick for the lip. Keep taking iron. Unrelated to your question: If you do not wish to be pregnant, use contraception all the time, every time. You may consider implanted contraceptive, or IUD. Practice safe sex. Get HPV vaccine.