You're right--they don't work very well. Cosmetics such as flesh-colored concealers do work pretty well, though. You can probably get a free application at a makeup counter of a department store. (Sometimes it's better to call for an appointment in advance. Any of the major cosmetics brands should be happy to accommodate you.) You'll probably be expected to buy something. This is optional, but you'll probably want to buy several products when you see the difference that a professional makeup application can make.
If you're still very unhappy, you could consult either a plastic surgeon or an ophthalmologist who specializes in plastic surgery about removing the bags under your eyes. This would involve an outpatient procedure not covered by your insurance. A cosmetic dermatologist might be able to reduce your dark circles with laser treatment.