Tylenol (acetaminophen) is an over the counter pain reliever that should not cause any sensation or reaction within the body that would cause one to become physically addicted to it. Long-tern use and excessive short-term use are proven to cause liver damage and have been implicated in kidney damage as well. You can overdose on tylenol or any medication. It is often compounded with narcotic pain relievers such as codeine or hydrocodone, to which a patient can develop tolerance and dependence.
Do not take tylenol for an extended period of time and do not take more than the recommended dosage. If you have a condition that requires more pain relief than tylenol affords, a physician can prescribe a narcotic such as vicodin (hydrocodone). Take this INSTEAD of tylenol, not in addition to it. If you think you are suffering withdrawal symptoms, it would be related to the vicodin, not the tylenol, but from what you describe it doesn't seem that you were taking that much.