Hi Tim Sedona and welcome,
To get current user you should use either the userName() function or SharePoint's UserProfileService, or Qdabra's Active Directory Web service. First two options are out-of-box. The People Picker is used to add users to your form that should get email notifications, etc. If you are trying to assign a form to a user using People Picker, you can integrate it with UserProfileService to query the names and get the groups, but it's a bit of a pain to extract the data if you have more than one user that needs to be selected.
Anyway, once you verify that the aliases (usernames) you get back from your People Picker plus UserProfileService query correspond to the actual column values in your SharePoint list of user/groups (note: I'm assuming this ShP list has group information in it but you could use the UserProfileService to get group info), you just set the group info in a field in your main data source and then add formatting on the section to hide if the current user is not in the group. You can look up the user by filtering the secondary SharePoint list data source or querying the UserProfileService. Take a look at Clayton Cobb's SharePoint Madness site for a great example of getting group info.
Eminently doable. Best of luck,