Welcome Olivia. I am sorry for your troubles. A complex cyst is one that contains both solid matter and fluid. They typically don't go away on their own although they can. Most are benign (non-cancerous) so if they are small and not suspicious looking, they will usually monitor them via periodic ultrasounds. But if they look suspicious or get too large (over 7cm or so) surgery is usually needed. If cysts are benign, it is best to have just the cyst removed (cystectomy) versus the whole ovary. This is important not only for fertility but also for the hormones that the ovaries produce our whole lives (yes long after menopause) to keep us healthy.
Be sure to make a list of questions to ask at your appointment. If you are like me and most patients, we get nervous and forget what we wanted to ask. Let us know how your appointment goes.