LOL Katnip, I really like to see those bags !
If you are healthy and nothing is really wrong with you there is nothing a doctor can do. Actually they are supose to tell you it's normal. If you go to a dermatologist or a beauty salon they will help you, but they will suggest much the same as people here, vitamins and topical products like creams and serums.
In hard cases like yours, you really need to do things systematically and keep up your skin routine every day for about three months to get full effect of any treatment. It is a long time, but improvement should come gradually and be visible sooner.
Still, I suggest you take a multivitamin with Vitamin K just as a regular diet suplement. If you suspect you are low on this vitamin eat 3 times "daily recommended dosage" for a month or so, and then step down to regular dosage. There are some indication that lack of Vitamin D is not helping this type of problem either.
Most off-the-shelf products will not help this problem at all, there are a few that has showed themselfs to be effective, and who really (!!) will help. I know of only the Hylexin brand, but there are others and perhaps some have tried a good one that they can recommend.
The creams that has a chance of doing something for you are often very expencive and are based on actives that are available from do-it-yourself skin care sites.
Two of the most important ones are called Chrysin and Hesperidin Methyl Chalcone together with peptides like matrixyl or sea weed extracts WILL help the discoloration. Try these ingredients in an eye cream, they will work if the problem is "leaking" capillaries. They are not that expensive if you buy them online and add them to you an eye cream you like. Have the products you used contained these ingredients? There are just a few ingredients that targets this problem, and not that many of-the-shelf products available containing them.
If it is overproduction of melanin there are lots more you can try, but choose your ingredients with a specific aim, and then change your strategy if it does not work at all. The theory here is generally focused on protecting skin from sun, using ingredients that inhibits melanin production and that reverse damage cause from sun like age-spots.
Sleep at night, get some sun and exercise in fresh air every day.
Now here is something new:
There are many miracle stories from people who went on the "Dr. Perricone diet", with severe darkening around the eyes. People who had these problems since childhood got rid of them. I have seen some really dramatic before and after pictures. It is a diet where you focus on eating foods that are anti-inflamatory (salmon, walnuts, vegetables, Omega3, foods that rate low on the glycemic index) and stay away from foods that in the long run cause cronic inflamation in the body (foods high in sugar, processed foods, white flour, french fries, pizza). This is suppose to relieve a lot of skin problems and result in a healthier, younger appearence. I am in the process of adjusting my diet to Dr Perricones recommendations
He also have lots of recomendations for skin care. He uses alpha lipic acid both as a food suplement and a skin care ingredient. It is all about getting tons of natural anti-oxidants and avoiding sugar and white flour.
Good luck Katnip