You're on the right path with AddColumns - you can use that to convert one of your table columns into a text one. In your case, you can have something along the lines of the expression below.
Search(
AddColumns(
TheItemsExpressionInYourGallery,
"CombinedCourses",
Concat(Courses, Value) // 'Value' would be the field name in a SharePoint choices column
),
txtFilter.Text,
"CombinedCourses"
)
Hope this helps. If it doesn't, consider replying with your current expression and the schema of the Courses field, as it will be easier for the community to help you if we see the data you are dealing with.