Suggest Remedy For Rash/exema With Dry Lips And Mouth

I have a rash/exema on the side of my left thumb after applying Neosporin it hasn't gone for ver 15 days .my lips are turning dry and itchy around my mouth and also itchiness on the bases of all my fingers in my right hand. I am 50 yrs old, I am g6pd deficient .my haemoglobin level is 7 , please advice