What you have just described sounds like post-inflammatory hyperpigmentation, or PIH for short. This is a pigmentation condition left when your pimple heals. While it is not a true scar, and will fade with time, this can take many months on its own. Pimples do not turn into moles; they are very different conditions.
You may be able to speed up this process by using some medical-grade creams and/or some procedures such as lasers and chemical peels. It would also be important to target why you keep having repeated pimples in certain areas of your skin too, to stop this cycle of pimples and post-inflammatory hyperpigmentation. You may wish to consult your doctor regarding possible treatment options for your acne condition.
Remember not to pick at your pimples too, as this can worsen PIH and even lead to scarring in some instances!
Dr. Joanna Chan