The addiction isn't to twitter. You feel like you will miss out on some important information if your access to twitter is blocked. You aren't browsing for no reason, while browsing a part of you has decided this is the best use of that time. Whatever else is going on isn't important enough to care about more than you care about seeing if there's new tweets.

If the people you follow stopped posting on twitter at the same time you changed your birthday, would you have cared about getting it restored? Valuing and caring about tweets people have sent isn't the same as being addicted to twitter. Maybe the problem is how much you value seeing those tweets the moment they are tweeted.