The drooping and browning that you are seeing on the branch tips of trees, including your dogwood is a result of the female periodical cicadas inserting their eggs into the branches. You can see a series of insertion lines on the underside of the affected branches on your dogwood. 

Your dogwood is not dying and the trees will be fine. This is kind of like natures pruning. Leave them for now. In about 6 weeks the eggs will hatch and the tiny babies will drop to the earth and dig in for another incredible 17 years.

The branch tips will eventually naturally drop on their own or can be pruned out later.

Christine