You can easily look up the estimated cost of shipping a bag from NYC to a Dallas hotel address.
https://wwwapps.ups.com/ctc/request?loc=en_US. You may need to also purchase a box to put the luggage in, but perhaps UPS would ship it as is with a shipping label securely attached.
But at ~50lbs and something along the size of a piece of check-in luggage, I don't think it will be cheap. And if you need it there on time, you'll be paying for at least 3 day select service.
I guess you have to decide if the cost of shipping the luggage outweighs (pun intended) the inconvenience of shlepping the extra bags around before you embark on your DFW trip.
The OP is contemplating shipping her bags from North Carolina, not NYC, since she will be in NC for six days.
From Raleigh/Durham, the UPS Ground service delivery standard is three business days to reach Dallas, so I would not pay almost double for Three-day Select, especially since neither service is guaranteed these days. (FedEx Ground is also three days from Raleigh/Durham to Dallas.)
If the OP can ship her bags a couple of days before leaving NC, I suspect that UPS or FedEx Ground service would be just fine, even if the bags were delayed a day or two. If the OP can only ship her bags on a Friday for Monday arrival in Dallas, I expect that the cost will be prohibitive.