That is not the bottle baby.
We have antibiotics but at this point bottle raising the lamb and culling the ewe is the appropriate course of action. There doesn't seem to be any rhyme or reason for when or which ewe will get mastitis.
The treatment for mastitis is to infuse antibiotics up into the utter through the tit. All of the infusers available are sized for cow utters not sheep utters. This is done for milk cows in an attempt to recover some milk production after the treatment has run its course. We struggle with the decision of which is better for the ewe, allowing the infection to run its course (which will not kill the ewe) or shove an oversized tube up the sheep's tits possibly damaging tissue.