SQL - how to find unique values from 2 columns?

Question

I'm using SQLite, and would like to get only rows with values that are unique per table. I know how to get values per each column, but can not create a single (sqlite compatible) select to get unique value from both column.

Here is data example:

col_A	col_B
111	777
222	333
222	111
444	333
222	555
333	666
333	777

My desired result from above example would be rows with unique values that include only: 444, 555, 666.

col_A	col_B
444	333
222	555
333	666

222 should not be in results as it appears multiple times in col_A. 777 should not be in results as it appears multiple times in col_B. I need only single occurrence of value in either col_A or col_B. Unique value per table, not column.

How far i managed to get:

SELECT * 
    FROM my_table
    WHERE 
        (SELECT col_A as asset from my_table GROUP BY col_A HAVING COUNT(*) = 1
         UNION
        SELECT col_B as asset from my_table GROUP BY col_B HAVING COUNT(*) = 1)
            IN (col_A, col_B)

I have tried with UNION and few other approaches, but can not achieve desired result.

Answer 1

WITH
  symetric AS
(
  SELECT col_a, col_b, col_a AS lookup FROM t
  UNION ALL
  SELECT col_a, col_b, col_b AS lookup FROM t
)
SELECT
  col_a, col_b
FROM
  symetric   AS t
WHERE
  NOT EXISTS (
    SELECT * 
      FROM symetric
     WHERE lookup          = t.lookup
       AND (col_a, col_b) <> (t.col_a, t.col_b)
  )
ORDER BY
  col_a, col_b

Demo ; https://dbfiddle.uk/9tzUASle