They called it minimal brain dysfunction when I was diagnosed, many, many years ago. Today it's called ADD or attention deficit disorder.
I've dealt with it all these years, without medication, but it has required some adjustments on my part, and some accomodations on the part of others.
There are varying degrees of this malady. I, too, have a difficult time finishing things and I get a little perturbed when I am interrupted in my classroom for things that could really wait. At times our guidance counselors and our curriculum coordinator just don't understand.... When I am interrupted, I have a time getting back on track. And it doesn't take a lot for my mind to begin wandering.
I tend to be a bit impulsive, have no shortage of very creative ideas, but cannot always manage to put them into practice.
I don't lose student work as much as you describe yourself doing, but that is because I have developed particular strategies for keeping that from happening. For example, I require that students put things they turn in into a basket I have on my desk, rather than giving it to me. I am also very meticulous about how students do their work and in what form, looking to reduce the amount of "loose papers" that can be mislaid. Much of what m y science students do is in a notebook, which I collect at least once each week. Even then I have a very precise and specified way to do it.
I'm up front with my coworkers and with my students. They know of my malady and I ask them to help me remember things.
Having MBD or ADD is NOT a death sentence. It can be coped with and lived with. One just needs to be up front and knowledgeable about their condition and look for ways to deal with it, without l etting it deal with you.