Since the nuvaring had fallen out many times and you had unprotected intercourse, chances of pregnancy cannot be ignored. There are sensitive urine and serum pregnancy tests which can detect hcg levels as low as 20 Miu for urine and 5 Miu for serum hcg test, as early as 8 to 12 days post ovulation. These are highly sensitive tests. The results can be confirmed by a pelvic ultrasonogram to visualize the intrauterine gestational sac and a positive fetal heart sound.
I’ll also suggest you an obstetric ultrasonography, which can pick up the pregnancy in the first 4 ½ weeks of pregnancy.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing