Try going to Settings>Misic>Volume Limit and after tapping on volume limit see if it's set to max. If so, try setting it at a lower level to see if that helps.
Take a look at Music - Sound Check. Disable or enable it, maybe there'll be a difference. Restart your device after changing it, let the changes take effect.
Also look at EQ. This affects all sound output. Try a different setting there. Also restart your iPhone after changing the setting.
What about Sound Check? Did you try changing this as well?
Try resetting your iPhone: press and hold Home and Power button until the Apple logo appears, let go of both and let your device power up.
And another idea: is your iPhone up to date? iOS 8.1.1 was released more than 24 hours ago.
If this doesn't help, reset all settings in Settings - General - Reset. You'll have to go through the Settings app again and choose your preferences, also the Volume limit, but maybe it will help with your problem.