Han's got infected one time and the only thing that would heal it was antibiotics. It looked really really sore.
Keep her nails as short as possible.
The thing that worked for us in the end was antibiotics, then strong hydrocortisone on any redness that flared up (I didn't like the thought of steriod creams but it got that bad

) but mostly trying to work on preventative measures once it was under control... like changing washing powder to sensitive or ecostore and moisturising in likely eczema patches about 600 times a day.
Aqueous cream did absolutely bloody nothing for us. Emulsifying was good as a maintenance thing but won't treat eczema. I had to stick with that tho as I couldn't afford to buy all the other lotions and potions!!
good luck!