What’s the pattern you have made? There is a small chance there was an error in the pattern which might be listed on ravelry or the designers website or someone here might know it.
If there was an error you might need to do a bit more than a new bind off.
Salmonmac gave some great suggestions for altering the full neck which you might need.
If it is ONLY the final bind off that is tight then a stretchy bind off can help a great deal.
Working in a larger needle really helps, so you can knit in your normal tension (not trying to be loose). If I knit in 4mm I might bind off with 4.5mm or 5mm, sounds huge and looks loose initially but once the stitches all settle in it works well.
Binding off in pattern helps, so if it is rib then following the rib with knit and purl bindoffs as they present.
An iceleandic bind off is nice and loose and I love the look of it. In this case I tend NOT to go up a needle size because in my experience the same needle size has worked nicely (try it out on a swatch)
There’s a couple of links.
You can also Google “stretchy bind off knitting” to find more tutorials and try out some different ways to see what you prefer.
Just wondering, did you have a bind off row BEFORE picking up to knit the neck band? This could be the tight area.
You could post a pic of your project too, to show how it’s looking now with the small neck.
…just had another couple of thoughts.
If you seamed the shoulders you could possibly undo the seaming and make the seam a bit shorter, leaving a wider neck. It depends how the sweater is constructed.
If the neck band is knitted in the round, I’ve seen a tutorial suggesting to knit inside out which makes the inside yarn travel a bit further (on the outer circle because its inside out) to guve a slightly bigger neck.
I’ve also picked up MORE stitches than a pattern says for a neck band. I am not very experienced in knitting but I got a nice stretchy neck band by having extra stitches. If you do this make sure to calculate the correct multiple of the rib you are using.