Agree - not showing an enlarging necrosis with sloughing of the dead cells. It’s been long enough to be at that stage. If it were me, I’d have the wife filling that wound repeatedly with hydrogen peroxide to reduce the local infection. After a few rounds of that, pack it with triple antibiotic ointment (OTC) and cover. The doctor will probably do a shot and some oral antibiotics while continuing wound care.Probably not a recluse bite then. Get it checked out.