If the infected teat is bloody or comes out bloody milk, its mastitis and you need to milk her out twice or three times a day and must warn you, it will smell BAD! Enough to make you gag but gotta do it. You can still let her nurse her kid off the good teat. She will be fine. The kid will have to be fed more often tho to make up for the bad side.
Congratulations on the new kid! Cute!