You can access your Outlook remotely by going to the Microsoft Online OWA link directly and logging in with your email credentials.

OWA link: https://red001.mail.microsoftonline.com

The Microsoft Online Services Sign In application is installed on each end user’s computer to provide a single sign-in point for Microsoft Online Services. The Sign In application makes it possible to sign in one time and then access services any number of times during the sign-in session. Without the Sign In application, end users must provide a name and password each time they try to access a service. Once logged in, you are able to access both your Outlook and OWA (Outlook Web Access) by selecting the appropriate link.