A music video where the singer (a guy) takes a picture of a girl and then tries to find her when she vanishes

I think you are referring to "I Remember You" by Skid Row. The impression I get is that she is dead (see cemetery at 1:26) and he burns the rest of the photographs at the end of the video, which leads to two possible outcomes. Either he has accepted the loss and is moving on, or cannot accept the loss and is giving up on life. See if this is the video.

https://www.youtube.com/watch?v=qjuEXKwnkLE