Hi This is dr.akhila,
Under eye dark circles could be because of various reasons its important to fund out the cause before suggesting any kind of treatments. To avoid tanning please start using a good medicated sunscreen( meet a doctor to check ur skin type and suggest sunscreen accordingly).
Next Steps
use a broad spectrum 30+ spf sunscreen and cover urself in the sun.
Health Tips
please have 2 to 3 lt of water to keep ur skin hydrated reduce salt intake to avoid any kind of puffiness under eyes. have food which is rich in antioxidants like papaya,pomegranate, tomato, green leafy veggies etc.