Hi - are you promoting the User's Name, Month and Year fields to your SharePoint library you submit the form's to? You'll want to do that first.
Then, create a secondary data connection to that library. Be sure to include the User Name, Month and Year fields in the data connection. Toward the end of the data connection wizard, you'll have the option to decide if you want the data returned when the form opens - deselect that checkbox.
Add a form open rule to set the Query field for the user name in the data connection you just created to the userName() function, and add another action to query the data source. You could also set the query field for year to the current year to get just this year's. That can be done with substring-before(today(), "-")
This should return a list of the items the user has submitted to the library.
From there, you can add rules to set the checkboxes or you can use default values for them that check to see if there is an item in the list with the correct Month name.