To me both ways are fine.
But a little aside note here: by saying "There´s a pounding in my head."
Pounding is a noun and in it could suggest that the pounding is recent or not. It is a song, afterwards you understand that it comes from a hangover or something like that, so most problaby from "yesterday", there is the music refers to some happening on Saturday morning/noon or around it.
Whereas, in my "my head is pounding" (pounding is a verb ended in ING, and in this case, it means that my head is pounding right now, at the moment I am saying that..
Answering your question, yes. In my opinion it could be used both without any harm to the meaning.
But I must repeat, in this case, it´s not always that the meanings intersect.