"Crossmaker" = cross + maker. The word seems to have been made up especially for a song, so there's no point in putting it in your conversation. People will wonder why you speak English in such a strange way. "Under my skin" is pretty much as Gareth describes - a strong influence on your thoughts, either positively or negatively. Look for the Cole Porter song, "I've Got You Under My Skin".

Being a crossmaker is a reference to the fact that Jesus was a carpenter who died on a cross. He could, conceivably, have made a cross. If someone is under your skin it means they are on your mind, or affecting you very strongly. It can often mean that someone is annoying you.