Generally a night terror is more easily passed through if nobody interferes with it. The best thing IME (as someone who has had them) is to just sit by the person until it passes, in case they wake and need comforting.
I can't help wondering whether your dd might be having some breathing difficulties, leading to reduced oxygen in her blood, and therefore the extreme NT. Think what it's like if you cover your head with the blankets - stuffy, uncomfortable, eventually claustrophobic, and you fling the blankets off not wanting to be covered at all, rather than just uncovering your head.
Is she on any medication for the asthma? Maybe it needs to be adjustsed. BTW I don't know much about asthma, so don't take my word for this, it's just what comes to mind readign your post.
HTH, and doesn't frighten - it's not meant to.