You can transfer files to your client however you like. As long as you get paid through Upwork, they don't care how you submit your work.
But I will say if the files are large, email is a terrible way to send them. It's a system that was never designed to send large amounts of data. A better option would be to use something like Dropbox, Google Drive, OneDrive, etc.
re: "Even on social media?"
Upwork has no restrictions about how you communicate or share files.
You are welcome to use social media to do so if that is how the client and freelancer prefer to do things.