The insect bite reaction which you had is called Paederus dermatitis.
If treated early by dermatologist, a pigmentation could have been prevented.
Next Steps
For the pigmentation, usually the depigmenting creams such as biluma cream help. But since the under eye area is very thin and sensitive I’ll advice u to use a milder cream or use biluma alternative night and less than a pea size.
Health Tips
Need not use the other creams and tablet.
sunscreen is complusory as this cream makes the skin sensitive.