Finding records between two Dates column in Oracle Sql

You may check for an overlapping range and refrain from inserting if one be present:

INSERT INTO yourTable (Start_Date, End_Date)
SELECT date '2022-01-18', date '2022-03-31'
WHERE NOT EXISTS (
    SELECT 1
    FROM yourTable
    WHERE date '2022-01-18' < End_Date AND date '2022-03-31' > Start_Date
);