No. Feeling unhappy is not addictive, but the behaviors that lead to unhappiness can be habitual. Our behaviors so easily turn into ruts or automatic routines. So, if our routines are not accompanied by feeling pretty good most of the time, we can establish new and happier habits. A good book on behaviors that tend to promote feeling ok or better is "the how of happiness." it's worth the effort!
Well also. Inability to feel joy maybe a subtle sign of depression. It can be hard to think one self out of depression & medicine sometimes is needed temporarily to help re-craft thinking patterns. Signs of depression in this sense are when old pleasures no longer lift your heart. Where seeing a friend, a sunny day, or a favoirte song no longer cheer you; this may be depression--not an adiction to misery.