Carolyn:
Livedo reticularis refers to a netlike pattern of redness and mottling. In most cases it is not associated with internal disease, and has neither cause nor specific treatment. When more blood flows to the skin (in hot water, for instance)or when the skin is chilled, the appearance can be accentuated.
Beyond that, there really isn't much more to say. If you're not comfortable with the dermatologist's diagnosis, perhaps you should seek another opinion.
Best.
Dr. Rockoff
I had mentioned that the under skin mottled look is only on the lower arms. Looking today, it is on the upper arms also. Thank You.