Father Is 80 Y/o. Has A Thin Red Streak Running

Father is 80 y/o. Has a thin red streak running down his face from eye to mouth. Was dx as poison ivy by NP about 2 months ago. Took antibiotics. Theory was some flew up and hit is face while he was mowing yard with ridding mower and then ran down face with a tear/sweat. Has not improved in last 4-6 weeks. Wondering if it's something else or if poison ivy can go this long (60-90 days)? Thanks.