I'd you're hitting most of the notes. It could be the quality of the recording, but your voice doesn't match Amy Lee's timbre-ly. You seem to be trying to get volume more than anything else, you need to put more of yourself in to it (wishy-washy musician terminology I know). Singing from your stomach, and really feeling what you are singing will produce a much better result than just trying to belt it out. More practice should help fill out your sound.
I actually really like this song, so have listened to the original many, many times, so I may be being overcritical, but I would like to hear more. If I was still in an active band and came across you, I'd certainly trial you as singer.