As far as dryness is concerned, use products specifically meant for dry skin. You can try using cetaphil
cleansing lotion and moisturising lotion to keep your skin well hydrated. For pigmentation as a general rule-
Avoid sun exposure
Use a good sunscreen and repeat application every 3 to 4 hours
Take antioxidant and vitamin c
You need to consult a dermatologist
as dermatology being a visual field
, the cause for your pigmentation and the treatment required can only be suggested after proper skin examination. Take care.