A brownish patch on top of my foot, maybe a centimeter long. Is it some sort of foot fungus?

Consult a doctor. Without providing a photograph one should be extremely careful with regards to hyperpigmented lesions. While, it can be something so mundane, one must be better safe than sorry. Fungus on the foot is usually scaly skin, sometimes red patchy skin. A newly found patch is likely a dermatitis of some variety. A quick visit to a dermatologist or podiatrist should give you an accurate diagnosis.
Maybe. You should see a doctor and have the area examined and possibly cultured to determine what it is.