The Nuva Ring is a device that delivers low dose hormones into the body which acts to prevent ovulation and thus prevent pregnancy. It works in the same way the as the birth control
pill. The only difference is the route that the hormone takes. The only advantage of the Ring is that you don't have to remember to take a pill every day which probably increases its overall effectiveness at preventing pregnancy.
Since the Nuva Ring contains that same types of hormones as the oral contraceptive pill, it has very similar side effects. I don't believe the major studies have been done to determine the actual risk of a blood clot with the ring, but most physicians assume that the risks will be similar. I should point out that in most young women, the risk of a blood clot while on birth control is low and should not dissuade you from using it unless you have another blood clotting disease, or if you smoke.
I suggest that you schedule an appointment with your OBGYN. The two of you can discuss your birth control method and how it compares to others in terms of risks of blood clots and other problems. I hope this is helpful.