It's okay to share and use alternative means of communication with your client. You may want to record main terms, deadlines and changes in Upwork Messages in case there is ever a dispute though.
Also, remember that it's very important that the client hires you on Upwork and you see a contract under My Jobs before you start working on the project. All payments also need to be made on Upwork.
Check out this post for more resources to help you started.