Not feeling productive, or perhaps more correctly purposeful is indeed a thing that can weigh on your mood. We, as humans like to feel that we have impact on the world and the people we care about. Lacking that, depression is not unusual. And probably a bit of what you feel.
A partial solution is finding a goal, even a small one that you see as valuable and worth doing, and working toward it.
It could be simple, like learning how to cook a dozen dishes. Or being able to run a set distance, or reading about a specific time in history in depth. Or it could be complex, such as working toward a degree, or getting the skills for a new job. But in either case, it can provide you with goal that you can mindfully move towards that has value to you. Even starting on a path, any path, can start to life that feeling you are having.
And the hair? Don't worry about it. I pulled a genetic illness in 2003 that made every hair on my body fall out. Now there was a test of ones self image 🙂 You are not what you look like. That's just a package, and hair is perhaps one of the most variable parts. Others pay it far less mind they you are.
Myriads