The itching is probably due to chiggers or some similar insect. Your County Extension Office can direct you to appropriate products for dealing with them. The best turf for your area is bermudagrass. However it is not very fond of shade. You might want to consider brightening the shade through selective pruning. I would start by adding soil as needed to smooth out the area to your liking and then establish the grass. The following web site provides more information on turfgrasses for your area.
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