Professor not replying to my email. Why?
Expecting an overnight reply to any email is unrealistic. He may have some issues of his own to deal with, given the worldwide pandemic. He will probably reply "in good time", but by his standards. 

Whether you are allowed to take a make up or not we can't say here. It is up to him and to the institution. I hope it is allowed and expect it would be given the family emergency. But the other things you mention have little bearing on the issue. 

But waiting a week after the missed exam wasn't wise, and expecting an instant reply after you didn't offer an explanation for a week is a bit "over the top". 

I suggest that you wait to see what the reply is. There probably isn't really a need for instant action at this point.