Most likely your Portrait Orientation is locked. You can easily tell by looking at the top of your phone, to the left of your battery info; if you see a lock with an arrow around it, your Portrait Orientation is locked. To unlock it, follow the following steps:
From any screen on your phone, quickly press the home button twice and your open apps should appear at the bottom of your screen. Swipe once to the right, and your music player should appear as well as a grey box with the same icon as is beside your battery info. Press the icon once and “Portrait Orientation Unlocked” will appear. Press anywhere on your screen and the setting will be saved.