I would like to know please whether or not I can look for exoplanets without a telescope.
No. With a probability nearly equal 1 you will not find any exoplanet with naked eye from Earth, even under perfect conditions like no light-pollution. The human eye simply does not have enough resolution to observe any of the closest exoplanets directly.
Neither of the methods of detection an exoplanet work without any additional tool (such as a telescope for any part of the spectrum).