Why am I getting brownish patches on my face?

Hormonal changes. This is "melasma" of pregnancy caused by excess melanin pigment production by the skin cells under the influence of estrogen and Progesterone of pregnancy. This is similar to what happens when some women take birth control pills. There is also a genetic predisposition, and exposure to sun can make this worse. The condition often regresses after pregnancy is over. Skin lightening agents may be used.
Many possible causes. Brown patches on your face is usually caused by either hormones, sun damage or inflammation (like with acne.) for fast results, it can be treated with a laser. Creams can be very effective, but take longer to work. The cream is proven most effective contains a 4% hydroquinone- a prescription strength. It is best to discuss this with your doctor to determine what is best for you.