How can I remove/cover up my dark circles?

I'm a teenager (and female) and I've had purple-ish/reddish dark circles for years. I've tried many different things to cover them up (tinted concealers, ect.) but nothing seems to work! When I apply concealer in the morning and feel like my circles are finally hidden, they reappear as soon as I step away from the mirror. They don't show up very well in pictures, but I feel so self concious whenever I see my reflection, since they make me look old (and not in a good way!). Are there any topical solutions (certain brands of concealer, ect.) for covering them up and/or longterm solutions for getting rid of them? Any advice would help! Thanks :)