Unfortunately Deb, its a myth that skin gets better after your teens. Many adults of all ages find themselves with the exact same problem you are facing right now and don't know what to do about it either.
The most important thing you can do to help prevent break outs is to cleanse, tone, and moisturize your face every morning and evening. You say you've been using a cleanser for over a year with no results. I would like you to change your product line. If its not helping then it is obviously not right for you. You said you are using a mild cleanser, if your skin is sensitive, that is great, find a cleanser for sensitive skin. However, if your skin is not sensitive then get a regular cleanser meant for your skin type (oily, normal, or dry). Sensitive skin cleansers may not be effective for everyone because they are so gentle they just may not clean well enough.
You also don't mention if you use a toner every day. Toners are very important and highly underused. When you cleanse your face you change the pH of your skin. Your skin wants to go back to its normal pH so will respond by making itself more dry or oily. If your skin becomes more oily then your moisturizer just sits on that layer of excess oil and doesn't penetrate. This can cause you to break out more frequently. If your skin becomes more dry it will actually need more moisture and your daily moisturizer won't be enough. This can cause dry skin and more blackheads because dry skin doesn't slough off like its supposed to so the dead skin cells hang around blocking pores, causing blackhead outbreaks.
When you choose a new skin care line I highly recommend using the cleanser, toner, and moisturizer from the same brand. Companies design their products to work together and you will typically be happier with the results if you use coordinating products.
To jump start your new skin care regimen I would recommend a facial with extractions. Your Aesthetician can remove the blackheads and whiteheads and give your skin a nice deep cleaning. She/he can also recommend a skin care line for your skin type if you aren't sure what you should be using.
If you can't afford a facial at this time, or if you need more exfoliation than just one facial can provide you may want to look into a glycolic acid peel. I recommend going to a place like Sally's Beauty Supply to get this. The people there should be more knowledgeable about their products than the average person working at a drugstore makeup counter. Typically the peels are available in 10%, 20%, and 30% formulas. If your skin is sensitive try the 10% peel first, if not try the 20%. I don't recommend trying the 30% until you've used the 20% and know how your skin reacts. When choosing a peel read the directions carefully. Many peels only get left on for a few minutes and then you remove them with cool water. Once you have chosen your peel and get it home, follow the directions regarding application and removal carefully. Leaving the peel on for to long can damage your skin badly. And do not use the peel more often than recommended. The peel I personally use says to use every day for 3 weeks and then use every other day.
The bottom line with skin care, you can greatly reduce the number of outbreaks you get by using the proper products for your skin but you can never totally eliminate them. Even I, the professional still get the occasional pimple. It stinks, but that is life, warts, pimples, and all :)
My last tip for when you do get your skin under control but end up with the occasional pimple in a very visible location. Wear a fabulous piece of jewelry. When I go out in one of my necklaces no one even notices the pimple smack in the middle of my forehead. :)
Deb, I hope I have answered your question.
If you have any skin care questions please be sure to leave them in a comment on this blog or email them to me at firstname.lastname@example.org.