This is black and white American movie of 60-s I believe. I've seen it on TCM channel about ten years ago. The story begins with a man trying to reach some address that is written on a piece of paper in his pocket. He is so distressed that he does not remember who he is and where he is going. He takes one taxi, then another, meets people who do not understand him. Some of them try to use him, some of them try to help him.

He slowly remembers his past live. He used to be a beginning piano player. A young inexperienced girl loved him. He tried to protect her from the world that he saw as evil and dangerous. He himself wanted to become a famous piano player. Then, he said to his girlfriend, we can have children. But this takes too long time, his girlfriend starts drinking, dating other men. He sees that but seems not willing to do anything: he is fully occupied with his work - achieving success in his career. Then late at night he comes from a concert and finds his wife in bathroom with her veins cut. Then he understands that the address on the piece of paper is the address of the hospital where she was taken. He rushes to the hospital. The last picture gives them gleam of home - he finds her still alive.

Cipolini, I could be wrong but at least I can attempt to take a stab at trying to help you find the movie. Some of your description doesn't quite fit (such as the piece of paper has a phone number on it, not an address) but I immediately thought of this movie when I read your question:
Mister Buddwing (1966) - IMDb user reviews

Thanks! I think this is the right title. I've seen this quite some time ago and may not remember everything correctly. Besides, I was not watching from the beginning of the movie.