I have the same issue. Don't know about the v shape, but I get a tenderness ONLY on one eye which is why I do not think it is a bacteria. It usually comes around allergy season which has me thinking it is allergy related. IT sometimes itches but if I tough it it gets worse and looks like someone poked me in the corner of my eye socket. I guess getting some antibiotic cream could hurt and would eliminate some possibility. Def not acne.
See a dermatiologist. Could be seborrhea, acne vulgaris, acne roseacea, etc.. or go hang out in the Derm forum
JCH MD