"It's tearing me apart" is different something that makes you sad, even something that makes you very sad. Someone says "it's tearing me apart" when faced with a grave/serious issue in their lives. Think about it, if you were to be literally torn apart, that would be quite serious, right? I say that to make a point, not to imply that people use this expression when literally being torn apart. The expression means that an issue is eating at someone's soul. It's a mind-consuming problem. It could make them sad, which is why it's tearing them apart, but it usually means more. Here are some examples in which this expression would be appropriate:
>Someone committed a crime and nobody knows, besides the person they're telling about the crime and saying this expression to
>Someone just found out their significant other is cheating on them but they haven't yet confronted them about it
>Someone is waiting for the results of an important test (whether its a licensing exam, medical biopsy, etc.)
>There's something on your mind that is bothering you and you can't think of anything else
You'll also see this vary with age. A teenager will likely think that asking someone out on a date and waiting for their response is "tearing them apart," whereas an adult wouldn't.
Those are just a few examples, and there are more many more where this would be appropriate. But as you can see, it's not an expression used lightly (unless as a joke). Save it for extreme scenarios/cases--something that is mind-consuming or eating at your soul.