I was another one who very rarely got any kind of hangover. When it did happen, it was because I drank something I didn't usually drink. I had maybe three or four hangovers in 17 years of drinking. Most of the time I was completely fine the next day. I used to wish I would get hangovers because maybe it would help me control my drinking!
A "hangover" for me was usually just being tired because I couldn't sleep a full night after drinking the day before.
Is it "normal" not to get hangovers? No, but being an alcoholic isn't "normal," either.