Mastitis can occur in newborns.  Indeed, abscess can occur in newborns.
But it is not caused by the maternal hormones.

Babies also get breast enlargment which is normal, and due to hormones
received *during pregnancy*, not lactation.  Why they should become
bigger during the second and third week of life is uncertain.  The
enlargement can last several weeks.  The appearance of the breasts with
this physiologic enlargement is different from mastitis.  There is only
slight redness, and there is no pain.  Furthermore, mastitis, as in the
mother, is usually one sided.

There is no reason, probably, for this baby to take antibiotics, though
I cannot be sure.  There is every reason for the mother to continue
breastfeeding.  Babies fed artificially also get this.

The physician, though assuring the mother she can continue
breastfeeding, dropped this one, probably not on purpose.  By suggesting
that breastfeeding somehow causes this, the physician has made the
mother is afraid to breastfeed.  How often do we do this?

Jack Newman, MD, FRCPC