I'm not familiar with AT&T, so forgive me if this is a dumb question--but do you mean that AT&T doesn't allow you to install apps from "Unknown Sources"? There's usually an option for that under Settings/Security.
Regarding the app, are you trying to update the app version itself, or update the data? If you're trying to update the app itself, are you sure that it is still compatible with Android 2.2.2? That's a pretty old Android version, so it's possible that your work app may no longer support it.