thanks for the query.
Having unprotected intercourse
while your period is going on, results in very low chances of pregnancy
Also, how long ago did you remove the Nuvaring
It is normal for the menstrual pattern to be altered a bit after removing or inserting the Nuvaring, as it is a hormonal contraceptive
So, please wait for a week or two, and if you still do not have a period, please go for a home ( urine ) HCG pregnancy test.
If that is negative, consult your doctor to find out the cause of absent periods.
Please switch over to any preferred method of contraception
again, if you do not desire a pregnancy.