She certainly can use the mikveh. She should speak in advance with the
mikveh attendant regarding her concern for infecting others so that she can be the last one to immerse that evening, and then the water should be changed. The risk of infection via the water is really minimal.
There is more of a problem with using the mikveh towels, so she should bring her own and do most of her preparations
at home. The risk of transmission is even less once she has gotten some treatment for the sores (generally antibiotics in a cream or by mouth).