Does Penicillin Injection For Sore Throat Prevent Scarlet Fever?

My daughter woke up with 103 fever. I gave her some motrin for the fever. By 2pm she looked worse and miserable with a bad sore throat and couldnt swallow without a lot of pain. I took her to her doc and was told she had strep throat and received an injection of penicillin. So is she pretty much in the clear that it wont develop into scarlet fever or anything worse since she has had the injection?