Who cares if she is engaged to the sperm donor. If he is over 18 then it's a case of statutory rape of a minor. 15 yo can't legally consent.
Not sure what you are asking about consent?
Your title states emancipation.
If she is truly an emancipated minor with the court documentation to prove it , then she has the legal ability to make her own decisions,
If no documentation then the parents or guardian should be contacted.
If they are not available, then a call to the ER DOC is in order to explain what is going on and asking them for permission to treat life threatening medical issues.
Pass the responsibility to the Doc & let them figure out the legalities.