Are they two separate email accounts, with separate addresses? One is a work address and the other a personal address? If so, you can access your web based email account from the browser, or from within Outlook.
If there are two, and Outlook is setup to handle both, you should still be able to access your personal web based account from within your browser. This is one way a company gets their employees enabled to receive email while outside of the office. Outlook is a client based email application and as such does not work outside of the system it is attached too, such as a domain based network with Exchange.
Employee's can use their work address while at work, or use the web based account while traveling. I know that Outlook has configuration option which can allow one address to be accessed both at the company network, and a web based section which allows that address to be accessed outside the work network environment.
If you use the same address for both applications then you need to setup your own personal account. You can add additional accounts to Outlook and use it as your private account. Outlook can handle multiple accounts, you just need to choose which one to log into when you start it up. You can configure it to open to a certain account, or have it ask you what account you wish at each startup.
Open the Outlook help options and ask how to setup additional accounts. Make sure your help has the Office Online feature turned on. That will afford you help on your hard disk and additional help from the Internet.
If you wish to keep your personal email separate from your work account in Outlook I recommend you simply open a free Yahoo, Windows Live, Gmail, or other web based account, or use the Windows Mail, or Windows Live Mail client applications. Windows Mail comes standard on Vista, and Windows Live Mail must be downloaded from the Microsoft Windows Live website. I prefer the Windows Live over the Windows Mail. Windows Mail in Vista repalced Outlook Express. You can turn Windows Mail off by going into Programs and Features, clicking on Turn Windows features on or off to the left of the window, and you access this from the Control Panel.
You can then go into your Set Program Defaults and set which mail program to be default. You can change this whenever you wish. If you need Outlook as your default at Work, turn it on in Set Program Defaults, and when you come home change it back to the Windows Mail or Windows Live Mail.
You can also set your default email program from within Internet Explorer. Open Internet Options, click on the Programs tab, and then simply click each drop down menu and select which one you want IE to use as default.
I hope I read your question correctly. I would have appreciated knowing which OS version you are working with as they differ on how to perform certain tasks and setup configuration options.
Good luck and have a nice day.