I would have problems with the background music too, I can't listen to music and read a book at the same time. I love to listen to music, but I tend to listen to music as an activity by itself, as I can't do other things simultaneously. If there is something else vying for my attention it keeps yanking my concentration away from what I'm doing and I find it very jarring and frustrating, unless I manage to concentrate enough to tune it out completely.
Sometimes I will listen to classical music to ease me into a task I am having trouble getting started on (it gives me something to listen to while I am trying to convince my brain to get into the right gear). However, as soon as I manage to find my focus with the task at hand, the music gets tuned out and I don't hear it at all. I choose classical music because music with words (or the radio, because people talk) is much harder for me to tune out and distracts me. I also don't like being able to hear people's voices or other noises - if I am deeply concentrating I won't hear a thing unless a loud noise makes me jump, but when I am trying to concentrate on something and not in that place of deep concentration yet that sort of thing will jerk me right out of what I am doing.
Try reading without the music, and listening to the music without the reading (I love to listen to music at night in bed, so that nothing exists but the music). You may find that it enhances your experiences of both and keeps you from getting a headache. 