I would usually tell moms with an abnormal NT result to relax and not worry, particularly if you had a normal first trimester screen and no others markers on the ultrasound.
However, while I don't think that you should panic and certainly this can turn out to be completely innocent, with a measure of 6.0 and additional concern on the u/s I think it would be appropriate to try to begin, for yourself and with your partner, think about a few "what if" scenarios.
What kind of further testing, if any, would you want?
Is a termination if this pregnancy something you would consider or would you carry a pregnancy to term no matter what?
How is your access to medical care, specialists if needed - maybe look around or ask for doctors in your area specializing in maternal-fetal med or genetic counseling.
For any definitive answer you need to talk to the specialist who will most likely recommend further testing. At this point in pregnancy you can have two diagnostic tests: a non-invasive blood test that uses the cell free DNA of your baby in your blood to detect Trisomy 21,13 and 18 (commonly referred to as MaterniT21 but there are a few other brand names). Or chorion villius sampling (CVS), an invasive test in which a small sample of placenta is used to determine the baby's chromosome number.
If you wait until 16 week you can also have an Amnio.
You can also decide to proceed with your pregnancy without further testing or only choose further Ultrasound monitoring which will be able to detect major organ problems, but not help diagnose any underlying condition.
It depends on whether you want to know "for sure" (really about 99% certainty) or whether you can live with the uncertainty and just take things as they come.
Again, by itself the NT measure is not a diagnosis of anything, but it indicates that there is an increased benefit from further testing.
I hope all goes well for you!
Good luck.