I honestly don't think there is anything wrong with dark circles. I've seen plenty people with them and I've just thought that they must not get that much sleep. Seeing as you go to bed pretty late, I can understand the dark circles. It's not a bad thing, I get them too when I don't get much sleep. You must be a hard worker! Just don't let the dark circles bring you down. I'm sure you look fine!
It depends on how old they are. If they're a little child then I think someone must be abusing or neglecting them. If they're an old person I just think "they're old". If they're between 18-60 I think they must need more sleep. I never think anything against that person. It's really not a big deal. BTW- maybe you should go to the Shisheido counter at your local Macy's (Nordstrom etc.) and try to get a match. It's an Asian brand and their products suit Asian skintones really well.
Honestly I don't usually even notice, if I do I don't pay attention to dark circles much. At worst I would think maybe you had a long night, but it doesn't really give me any particular idea about you as a person or think the person is ugly or anything?
I think maybe you should go to therapy. Something like this should not make you so upset or self conscious, my guess it that this issue might be more related to how you feel about yourself in general rather than the dark circles specifically?
But for concealing them- go to makeup counters at department store, or go to Sephora or a similar store that sells tons of different brands and have them help you find a good color match for your skin tone. I think Prescriptives and other brands/companies can sometimes even mix you a custom color for some things too? Also look at Shiseido, like another answer said.
I have dark spots under my eyes too, and I have never felt that way. If you really feel down, put sunglasses on, but I think you should be proud of what you have.