Why have they not gone yet?

Hello everyone! I'm new to this forum and wondered if I could get some advice here.

I'm a 34 year old woman and I have a reasonably healthy Diet and lifestyle. I've been getting spots and pimples since the age of 13 and can't understand why they haven't gone away by now. When I was younger I used treatments, like Benzyol Peroxide but I don't use anything now as my skin has got quite dry as I've got older and I have to use a lot of moisturiser. That's also something I don't understand - how can I have dry skin and spots?

Anyway, this is driving me mad. Will I have pimples for the rest of my life or is there a cure for adult Acne that I haven't heard of yet?

Thanks in advance for any replies.