It's actually a very normal feeling. It's not even comparable to other purely psychological addictions(like internet), because physical activity induces a secretion of endorphines. If the activity is intense, and lifting heavy weights falls under that category, the amount released is proportionally higher.
I have experienced the same feeling you described. I remember a few years ago I twisted my right ankle 2 times in one year - I had to quit sports for 6 weeks, and then build up gradually. I actually turned to alcohol to stop that nauseating and depressing feeling. I drank regularly much like an alcoholic, at least a liter of beer a day, often more than three (starting at lunch). When I recovered I stopped drinking as quick as I began.
This of course add's up with the normal 'pull' to do the things we enjoy doing. It's a craving feeling, that can get so strong as to provoke debilitating symptoms during withdrawal. The entire concept of addiction is very complicated and equally interesting, the dilemma about when an activity or a substance (not just drugs but also chocolate, ice cream, sparkling water) is to be considered a negative addiction will probably never be solved. You have to evaluate if the activity has any negative impacts on your life. Sports doesn't really fall into that category, so I wouldn't worry too much about it. However you may have noticed that it's more difficult to maintain a social life outside work and the gym, because you spend so much time there. Also having a relationship might not be so easy.
Fortunately in my experience the more sports I do, the less I feel the need to sleep. That really compensates for the time spent cycling or lifting weights.
Of course, everything depends on you perspective on life. I am sure you'll even find doctors that can diagnose some psychological disorder just because you love working out to the extent where you feel bad without it.
What causes that feeling?
To sum up this, perhaps, too long answer. The cause of your feeling is twofold:
- Physical withdrawal for the sense of well being that comes with natural endorphines.
- The intense craving for an activity simply because you enjoy it (this point is not to be underrated).
I wouldn't worry too much. Hang in there and always be careful with extremely heavy weights. The price we pay for bad form or for exaggerating always comes many years later (no complaints now does not imply what we are doing is good for our joints, ligaments and skeleton).