What over-the-counter medicine can I use to permenantly treat vaginal dryness?

No OTC's. There are no over the counter remedies to permanently treat vaginal dryness. You can use otc vaginal lubricants to help your symptoms but for a more long term solution you'll need to talk with your doctor. If you are post-menopausal topical estrogen cream may be helpful.
Not Permanent!! Of course, lubricants like k-y jelly (and astroglide is an excellent choice too!) work well for relief of vaginal dryness with sex. There is also an otc product called replens that is a more long-lasting solution to the problem but it still needs to be used 2-3 times a week. It uses a "muco-adhesive" technology that takes much longer to wear off.