K.,
I have eczema on my hands. I've tried several different things through the years in addition to prescription creams. When I have a flare up and my skin is raw I switch between the prescription cream and Neosporin. The Neo seems to help heal the area and allows the presciption med to do it's job.
Recently my daughter was diagnosed with Impetigo (a skin infection) and was prescibed Bactroban (generic-Mupirocin) to clear it up. The doctor described it as Neosporin but 10x better. I decided to try it one night and found my hards have cleared up better than anything I've tried - after one treatment!
My eczema is triggered when I've allowed my skin to get too dry. So, I wear gloves when washing the dishes or cleaning the bathroom, etc. I also use a good lotion at night to moisten the skin. Another suggestion is to stop using antibacterial hand soap as it also contributes to drying the skin. I hope this helps.
Good luck and hang in there!