Oracle 18c

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CREATE TABLE MYTABLE (
    id     INT
           GENERATED ALWAYS AS IDENTITY
           PRIMARY KEY,
    Field1 VARCHAR2(30),
    Field2 NUMBER(10)
);
CREATE OR REPLACE TRIGGER mytable__not_repeat_f1_and_f2
FOR UPDATE OR INSERT ON MyTable
COMPOUND TRIGGER
  TYPE MyTable_Fields_Type IS RECORD(
    rid     ROWID,
    field1  MyTable.Field1%TYPE,
    field2  MyTable.Field2%TYPE
  );

  TYPE MyTable_Fields_Table_Type IS TABLE OF MyTable_Fields_Type;

  fields MyTable_Fields_Table_Type := MyTable_Fields_Table_Type();
AFTER EACH ROW IS    
  BEGIN
    fields.EXTEND;
    fields(fields.COUNT) := MyTable_Fields_Type(
      :NEW.ROWID,
      :NEW.Field1,
      :NEW.Field2
    );
  END AFTER EACH ROW;
AFTER STATEMENT IS
    num_field1 PLS_INTEGER;
    num_field2 PLS_INTEGER;
  BEGIN
    FOR i IN 1 .. fields.COUNT LOOP
      SELECT COUNT( CASE WHEN Field1 = fields(i).Field1 THEN 1 END ),
             COUNT( CASE WHEN Field2 = fields(i).Field2 THEN 1 END )
      INTO   num_field1,
             num_field2
      FROM   MyTable
      WHERE  ROWID != fields(i).RID;
     
      IF num_field1 > 0 AND num_field2 > 0 THEN
        RAISE_APPLICATION_ERROR( -20000, 'Cannot have duplicate Field1 and Field2' );
      END IF;
    END LOOP;
  END AFTER STATEMENT;    
END;
/
INSERT INTO MyTable ( Field1, Field2 )
  SELECT 'a', 1 FROM DUAL UNION ALL
  SELECT 'b', 2 FROM DUAL UNION ALL
  SELECT 'c', 3 FROM DUAL;
3 rows affected

INSERT INTO MyTable ( Field1, Field2 ) VALUES ( 'b', 3 );
ORA-20000: Cannot have duplicate Field1 and Field2
ORA-06512: at "FIDDLE_EZWUCVJMSBXNCJZEORDM.MYTABLE__NOT_REPEAT_F1_AND_F2", line 33
ORA-04088: error during execution of trigger 'FIDDLE_EZWUCVJMSBXNCJZEORDM.MYTABLE__NOT_REPEAT_F1_AND_F2'

INSERT INTO MyTable ( Field1, Field2 ) VALUES ( 'b', 4 );
1 rows affected