Yep, migraines is the first thing I thought of. When I was diagnosed with them 20 years ago, I was convinced I had a brain tumour. My GP asked me to describe the pain and I did and said: and always on one side, that's what's so weird! And he said: that's a migraine. Migraines are 90% of the time on one side of your head.
Mine also usually on the right side, but I have them on the left sometimes too. They always start behind my eye, and if I don't treat them they pull all the way to the back of my head over one side. Definitely not a brain tumour!