Brief Answer:
To rule out causes . Detail follows
Detailed Answer:
Dear Friend
Welcome to Health care magic. I am Dr Charu , I will shortly try to help you with my opinion.
Allergic rhinitis is itself very commonly associated with 
dark circles. 
There are many treatment options for dark circles and perioral 
hyperpigmentation.
Some people get very good results and some do not respond much.
I need to know
1. Your job profile and working hours
2. Sleep patterns
3. Are you taking any medications for any other condition
I usually prescribe skin lightening creams containing kojic acid, vitamin C, arbutin, licorice. Along with it,  sittings of 
chemical peels containing drugs like kojic acid and lactic acid are given in between.
Usually very good results are seen.
But in some cases, when it is constitutional or hereditary, it does not show good response.
Also i suggest you to get 
Hemoglobin levels, serum ferritin levels.
In conditions like anemia , additionally iron supplementation is required along with these treatment options which i already mentioned.
I hope i am able to solve your query. Review with the questions i have asked and investigations.
Good Luck.