Yes. Sin is the breaking of God's Laws (as supported by 1 John 3:4). It's a willful act of rebellion against God and contempt for His holy nature. When we lie, steal, commit adultery, etc., we are breaking His law, and thus we are sinning.
God's Word makes it clear that none are without sin, and every one of us falls short of the glory of God. This is why we are saved by the grace of God made available to us through Christ's sacrifice when we believe and repent of our sin. Man is incapable of saving himself by his works.
Feelings, though, are not something we can control. They aren't willful acts, nor are they actions in any other sense. Granted, I'm sure that one could act sinfully because of one's apathy (I very much like the example DeepThoughts contributed from James 4:17), but I don't see any scriptural evidence that supports that the feeling of apathy itself is a sin.
I don't think a feeling by itself could be considered sinful. Feelings may even tempt us to commit sinful acts, but they are not sin in and of themselves. Sinful acts are sinful acts. There are many feelings that God doesn't wish upon his children--sadness, pain, grief, anger, etc.--but that doesn't make these feelings inherently sinful. In fact, God himself has felt anger (when his children deliberately disobeyed him) and sadness (when he sent the great flood). Jesus has felt these things, too, and was even tempted by Satan. But neither God nor Jesus have sinned, despite having felt these things.
A feeling only leads to sin when we act sinfully upon it. For example, a feeling of attraction to a person isn't sinful. God created us to be able to appreciate beauty as He does. But we would be sinning if we chose to entertain this feeling of attraction in our minds as lust. Does that make sense? I hope I didn't make this more confusing...