Shadow moustache, how to get rid of it?

When I shave my face with an shaver, it looks clean shaven, but after few minutes the upper lip becomes "black". As if I haven't shaved at all! This is a problem, because there is an transparent black line across my upper lips (it looks quite silly). I have tried everything and now I am picking (tweezing) to remove the hair from my upper lip. However there is a still black line (even though there is no hair). How long should I continue picking the hair? Are there anyways to decrease this shadow moustache effect? I have no other problems with chin or so on. Please answer!