Heya! Billie Jean is a wicked mistress.
I have skipped it… practiced a bit every single day… landed medium… still haven’t finished fast.
It is a song that has some precision and speed requirements. Nothing blocks you from skipping and and return as you feel more confident. 
Plow through and come back at a later date. Don’t work on a song when you are frustrated, it will be worse… go for an easier one… and build back up.
Get back in the shed!