I get a headache when I listen to a song using only one side of my earphone. Is this normal?

Headache with music. I depends on the loudness of the music or the type of music , if you like it or not. Seriously, one side of the hearing can beige sensitive than the other. Do you get dizzy with loud noises? I would get your hearing checked at an ear most and throat doctors office. Try not to aggravate your head with listening to music on that side. Feel better.
No. One ear may be more sensitive to sound than the other. This "hyperacusis" can manifest as discomfort, ear pain, or headaches w/ loud noise. It is usually associated with some form of hearing loss related to previous noise exposure. If it is bothering you a lot, you should see an ENT and your ENT will likely order an audiogram to test your hearing.