Using the assumption that playlistTextArea is your problem test box, the problem seems to be:
playlistTextArea.append(songName + " - " + songArtist + "\n");
You're reading the file lines one at a time, and then appending the entire list every single time, which will result in the pattern 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, etc. Easiest way to resolve this would be to make sure you clear the text box before the for loop (i.e. - Move to the playlistTextArea.setText(null) down).