Alternatively the skin issues could be separate from the thyroid. Please read up on PCOS and see if it fits. Ask your doctor about it. Polycystic Ovarian Syndrome is more commonly seen in people with thyroid issues.
Oily skin and acne are symptoms of hyperthyroidism (overmedication), not side effects of proper doses of levothyroxine. Perhaps your meds need to be reduced??? Do you have any other hyper symptoms? If you have recent labs, please post with reference ranges, which vary lab to lab and have to come from your own lab report.
Do you know the cause of your hypothyroidism?