You should be fine. There are tons of women who do things like drink, even binge drihnk, or do other recreational drugs that are 10 times worse than that before they realize that they are pregnant. I am not that familiar with darvocet but I was prescribed a narcotic painkiller throughout my entire pregnancy and my baby was fine. My ob/gyn prescribed it and it's quite commone believe it or not because most opf thise medications are tylenol based. Doctors usually care concerned with the infant being born with a dependence if those drugs are taken within the last few months of delivery. There are no real adequate studies on pregnant women and narcotic pain killer because who in their right mind would have a study full of pregnant women but there are no real reports of adverse effects on the fetus if the mother takes those drugs as prescribed and for a short term.
I would talk to your dr to make yourself feel more comfortable though but I'm sure eveything is ok.
Congratulations on your pregnancy!!
As long as you're stopping it now before vital organs are developed, then everything should be just fine. Congratulations on the baby and hope your neck pain is better.