Of course it isn't normal but too late now. At least you have plenty of company, and there are worse addictions...Much worse addictions. 
I dream of chess!?!
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Don't worry. Chess addiction does not last so long.
It's called obsession & many strong players do it. Nothing wrong with it as long as you know what you want & it doesn't interfere with anything more important. I've known some players that were that way. Zakhar Fayvinov was a friend of mine (originally from Leningrad & moved to U.S. well into his 50's but was much stronger at a younger age. He peaked at about 2400 here) & he used to tell me that when he was much younger (still improving) he would constantly do tactics puzzles on the train every day, when he took breaks, when he had some extra time. Endgames & tactics. He would learn endgames inside out as well. Sure, I bet a lot of aspiring masters think about chess a lot during the day, even when asleep! Just put it to good use & don't let it be a waste of time.
edit: it's been a long addiction... even before the movie searching for bobby fischer and still to this day!
Seek professional help. Chess obsession usually last not more than 2 years for non-professional chess players. Many pros suffer endlessly.
If all of this energy could be put to use in the real world Mandy & Ken would likely be big time. Like that woman who abandoned chess to become a millionaire poker champion. Talk about dreaming!
Is it normal to think about chess all day long? Play tactics trainer on lunch break, coffee break, bathroom break etc.