You are correct that the NuvaRing should be removed prior to immersion.

After the fact, and once you are home from the mikveh, your tevilah with the ring is acceptable based on two mitigating factors: one, the ring is located in beit hasetarim, a hidden place, which is treated more leniently than other body parts with respect to chatzitzah; two, the ring is mobile while in position, theoretically allowing water to reach the area around it. Thus in this case, your tevilah is valid and you need not immerse again.