Hi, may I make some suggestions? I would change the first verse to "You can't come next to me" because "You can stand next to me" would be "Voit seisoa vierelläni" and it has a quite different meaning (and the next verse needs a little fixing in that case, too).
"Katson linnunrataa yksin" --> "I watch the galaxy alone" (or Milky Way to be more specific)
"I always had to shine" --> maybe "got" instead of "had"?
"Joku kyyneleeni poistaa / Huulillaan" --> "Somebody will remove my tears / With their lips"
"Saa vain haavan ikuisen" --> "You only get an eternal wound"
"Itkien, nauraen vielä jaksaa silmät palaa" --> "Crying, laughing, still the eyes manage to burn"
"Kuultaa" is more literally "be dimly visible/translucent" etc. but "shines" can also work.
"Kun kaikki on jo menneet" --> in this case "kaikki" more likely refers to people, so it could also be "everyone" and not "everything"
"joiden kasvot tunnetaan" --> the faces are commonly known or not by anyone specific at least ("tunnetaan" is in passive), so "whose faces are known"
"Läpi silmistäni tuulee" --> "The wind blows through my eyes", and the wind goes to the empty room
"Sävelen, jota en / Jaksa enää toistaa" --> "A melody / Which I don't bother/care to repeat anymore"
And finally, "Joku kyyneleeni poistaa" --> "Someone/somebody will remove my tears"