What you are referring to is known as chloasma or melasma, and is
indeed a side effect of the pill. Although this condition is not dangerous, it
can be cosmetically displeasing, and occurs in a fair number of women taking
oral contraceptives.
The synthetic estrogens in birth control pills cause your body to be more
sensitive to ultraviolet light, just as pregnant women are. For this reason,
the condition is sometimes known as the "mask of pregnancy."
Basically, sun exposure will stimulate melanin pigment cells more than normal
(and often in an uneven pattern). Some women even develop a dark line down
their stomach which is known as linea nigra, meaning "black
line" in Latin.
The first thing you need to do is to limit your exposure to the sun, either by
wearing protective clothing or using sunscreen. You should also speak to the
doctor who prescribed the Pill and tell him or her about these side effects.
Changing brands or switching to a lower dose is often helpful.
Although these blotches will usually fade after you change pills and/or get out
of the sun, some discoloration occasionally remains. In those cases, a
dermatologist can recommend various skin bleaching agents if the blotches are
still very visible.
I know that you are feeling self-conscious, but this condition is not dangerous
and will fade over time, so try not to be overly concerned.