That isn't much information to work with but my first impulse is thrips. Take a sheet of white typing paper and hold it under one of the affected branches and shake the branch (don't go crazy, all you need is some short, sharp motion). If you have thrips there should be tiny moving spots left on the paper.
I don't think the Viburnum Leaf Beetle has reached North Carolina yet so you shouldn't have that to worry about. It also doesn't sound like their work. Short of the VLB insects and arachnids usually don't cause serious damage to Viburnums. I suspect you would do more harm than good by spraying.
Your description doesn't sound like a fungal issue. Be grateful for that.