I made the same mistake. I suspect the meaning is different even though the preposition is a clear cognate. To ask after meaning the same as to ask about someone (i.e. how they are, or what they are doing), not asking for someone (i.e. a request or summons).
The statement "actor x is asking after actor y" means that actor x is asking for actor y, at least in native English. It could be that this is a idiomatic part of the language, but I certainly would say, and expect others to understand, the saying "she asks after you"
In English to ask for someone means you want to see them, but to ask after them means you want to know how they are. The two things are rather different, but which is the sense of the danish statement?
In Danish, this exclusively means that she is asking to see you. The other use would be "spørger til". "En pige spørger til dig" would mean that a girl is inquiring about you - e.g. your situation or condition.