I use the nuvaring and have been on it since I had my daughter which was 3 years ago, can it cause cysts to form on my ovaries?

Probably not. Generally the NuvaRing or pill, as opposed to the iud, reduces the liklihood of ovarian cysts. The NuvaRing and pill work by preventing ovulation and the development of pre ovulatory cysts. The iud or the progestin only pill doesn't prevent ovulation as well - and works by thickening the cervical mucus.