Facebook addiction leads to many health problems and these are mentioned below:
Anxiety: A study by Edinburgh University found that about 12% of heavy Facebook users feel anxious and troubled. Their study also linked stress and burden with having a high number of Facebook friends.
Discomfort: Many people who were interviewed about usage of Facebook said that checking the timeline, wall posts, messages, trending topics, notifications, etc. gives you discomfort.
Brain: Another study found that people addicted to internet including Facebook have 10-20% smaller brains in the areas responsible for memory, emotions and speech. This is indeed astonishing
Desperation: Receiving no response after messaging someone, or posting on someone's timeline is horrible and makes you feel desperate and angry, a researcher observed.
If you are addicted to Facebook, you might have noticed some symptoms. Actually, Facebook addiction has become too much common, its addiction has been officially named as Facebook Addiction Disorder (FAD). You may read about FAD and the symptoms of FAD here. Also, I recommend you read How to Overcome Facebook Addiction?