I sometimes have the same symptom. (I'm 51) I do a few things to loosen it up. I've some hand weights that I swing thru my throwing motion before I leave the house. ( slow...think more like stretching) I do slow neck rolls clockwise and counterclockwise slowly working thru that tight spot on right backside of my neck. On the course for the first hole or two, as I'm walking to my throw, I keep my shoulders squared towards where I'm walking and turn my head 90-100 degrees left and right. I also do the old gym class propellor stretch, holding both arms parellel to the ground and rotating them in both directions....you can do this while you're walking. I'm usually warmed up by the end of hole two. Thats this winter, where there's not a lot of time or space to find a clear practice field.
Summertime, I definitely do at least 30 minutes of practice throwing, either in a field near the course or if possible on open holes on the course. Working up from like 70% effort to full out.
Hot shower, icing the sore spot...ibuprofen.