Can exercises to build up the trapezius muscle exacerbate neck pain?

Yes: If you have an underlying painful neck condition, i.E degenerative disc disease/pinched nerve/disc bulge; performing aggressive trapezius strengthening exercises can aggravate it. Try and do strengthening exercises with out weights. Consider working with a knowledgable physical therapist to make sure you are doing the appropriate exercises. Discuss with your md if pt is recommended.