What does he mean by "cover me up"? Could it mean "hold me" as in "embrace"? or "protect me"?

Native speaker’s answer
Rebecca
Yes, your guess is correct! The "cover me up" in this song can be interpreted as "embrace/hold/hug me" or "protect me." Typically, we use "cover up" in two ways: to indicate the physical definition (i.e. to cover oneself with a blanket or be embraced), or in the emotional sense (i.e. protect me, make me feel safe). Ex: His love covers me up and makes me feel safe. Ex: It was very chilly at night, so I covered myself up with a blanket.