What diseases/conditions can cause a red nonblanching line to appear on your skin (>3 months). dr said it's very unusual and doesn't know what it is

The key:nonblanching: In general, a red lesion that loses its redness when pressed is "blanchable" and is due to dilation of blood vessels. Non-blanchable red lesions are due to the presence of blood/red blood cells outside of blood vessels/extravasation. After 3 months this should resolve/fade. I presume your doctor is a Dermatologist. If you have no other symptoms/signs, I, too, would observe. Best wishes:)