lolWe'd need to know more about the song lyrics. I don't think this is a usual expression, it's poetic.
I think 'swell' means two things: 1) big, over-sized, inflated 2) fine, nice, great, wonderful, awesome... (a slang word)
So swell-headed could mean having an over-sized head, meaning the person has an over-sized opinion of him/herself. But possibly the songwriter agrees with this, and thinks the person is great.