I'm not familiar with your hosting company, but I don't see why you couldn't set it up to fetch mail from a specific account. To achieve this type of functionality you would log in and goto the admin panel.
goto Emails
Setup the email address that you want to check here.
Make sure that you configure pretty much everything.
How it is setup is fairly subjective based on how you want to do it.
Personally we use IMAP and an account on our Exchange server.
This URL may assist you also:
http://osticket.com/wiki/Email_Settings(http://osticket.com/wiki/Email_Settings)
Note that if you have more then one email that each email address can be configured to default the ticket to is own department. Just set New Ticket Dept. to the Dept you want. OST will not sort tickets based on the content of the ticket.
Then click on Settings -> scroll down to Email Settings
ensure that "Enable POP/IMAP email fetch" is checked.
ensure that the drop down boxes match your needs.
I hope that this gets you started, feel free to post on the forums if you get stuck. Good luck!