I would turn your water heater up all the way. Ours up all the way hits 140 degrees, it's gas. I've always heard 135 was the temp for disinfection (to a limited degree).
My dd at 7 days old had Impetigo, it's a staph infection. I gave it to her as I harbor staph and in stress will break out (like those with dormant GBS or herpes, it just lives in me).
They gave my dd oral antibiotics, maybe it was worse. It was on her thighs and the trunk of her body, it started on her back shoulder. It really was terrible looking and scary, since she was so young.
It is very contagious. It needs to be taken very seriously. And I would either boil my diapers (in addition to TTO in the HOT wash) or use CPF that I would bleach until the infection is gone and obviously the CPF after 2wks or so of bleaching would be trash.
I don't use bleach in my house for much, a bottle last me a long time. I do prefer to use TTO, vinegar and baking soda -- but I also know staph is a serious infection, one strain is the 'flesh eating disease'. You don't want this to get out of control.
I would in this case use a mild bleach water solution to wipe down diaper changing surfaces. I would limit diaper changes to 1 location. And I would be sure that if it spreads her clothes cover the sores to avoid contamination of furniture, toys, her scratching or picking, etc.
I've had staph break out on my face. I treated them with straight rubbing alcohol and straight TTO, I do not suggest this for a little kid -- it hurts like h-ll, but felt good at the same time do to the itching of skin healing. The last one I had, I ended up with red heat infection under the skin of my jaw line and had to go get antibiotics at 2 mo PP. My face looked horrible for months.
I believe mastitis is also staph related in some cases. I had mastitis when my dd was 13 months old and it kicked my butt!
So point is Staph is serious and to ensure your dd's health and healing, please take serious precautions to avoid creating a stronger strain.