The skin above my lip has started to darken, what are some homeopathic remedies I can use?

Individualized. More information is needed to answer your question. This includes specifics about the symptom (e.g. Brown, black, yellow, red, spotted, etc.) and general health issues as well. For instance, if the discoloration has come about since using birth control pills you might benefit from sepia, along with discontinuing the medication.
Adrenal or PCOS. Hormonal imbalance either due to adrenal issues or polycystic ovaries have this evaluated by drawing dhea and cortisol levels.
More details please. What do you mean? What are you reporting? What is the size of the area, raised, flat, intermittent, or persistent.? Sunburn, new lipstick, or makeup? What impact does this have on you?