Infections can also occur from uneven feeding. If she is eating on one side more than the other and the milk is staying in any particular breast for too long, that can cause an infection. I recommend pumping off an excess milk in the future. That's what I always do and I get a great supply in the freezer!!
No - it wont spread to baby. I assume you are breastfeeding and if this is the case, the breast infection has likely resulted from bacteria from your baby's mouth. It is important to keep breastfeeding and/or pumping with a breast infection to prevent milk duct blockage.