Since my radiator was never changed or unclogged and its’ replacement cost was almost the same as trying to unclog it, I went ahead and replaced it. At the same time I got the upper and lower hoses replaced as well.
The old radiator looked dirty once it was removed. I took a car for a drive that it did overheats whenever i go there before. Good news: the car did not overheat.
So it looks like culprit piece as ‘GeorgeSanJose’ thought was indeed the radiator.
Thank you every one for your tips and responses. They did steer me in the right direction. Very much appreciated.