Administration rights let you install software and patches - but this means that malware can also install and run itself to, for example, exploit unpatched vulnerabilities and even compromise the whole network. High risk activities should not be undertaken when running with administrative rights...and reading your email and browsing web pages are both considered high risk activities.
According to Microsoft's TechNet advice, the only way to be sure that a compromised PC is thoroughly cleansed is to wipe your hard drive and reinstall all software. If your computer has been compromised, seek advice from the IT Service Desk immediately.
If you are unsure whether you are running with administration rights, seek advice from the IT Service Desk. If you do have administration rights, you should have been advised on how to minimise risks by the IT Service Desk: if you have not been informed, again contact the IT Service Desk immediately.
If you have administration rights on your UoB computer then it is your responsibility to ensure that it is not compromised - remember, if software can be installed on your computer, then so can malware. The ideal advice is to arrange to get your PC properly managed by contacting the IT Service Desk.
You can apply to have Elevated User Rights (EUR) if you have a work-related need to install software or make other administrative changes to your computer.
You are almost certainly running with administration rights on your own, non-University-managed computer, though there is increased security on post-XP versions of MS Windows. For further information on what is provided and on how to minimise the risks: