How do i get rid of those dark purple circles around my eyes?

Decongestants: The blood from the face drains alongside the nose as it flows back to the heart; if there is a lot of nasal congestion, this puts pressure on the veins, and the blood backs up. The skin under the eyes is so thin that you can actually see this pooling of blood. Relieving the congestion opens up the blood flow, and the dark circles go away. See an allergist if otc decongestants don't help.

Infraorbital shiners: Anything that can cause nasal congestion can cause the dark circles under your eyes. The answer is to find and treat the underlying cause - allergc rhinitis, non-allergic rhinitis, etc. This is the bread and butter of what an allergist does.