Update to my slow leak issue:
So I went to New Capitol Tire in Kapitolyo after dropping my wife and son at Capitol Commons. They dipped the tire in the water and found the small hole (since there were just small bubbles coming out). The culprit was a headless screw, about a diameter of 25 cents coin in length. They applied a liquid cement and cold patch and problem solved. Tested the tire in the water again and no bubbles came out anymore.

I took the headless screw as a souvenir/remembrance of my first tire hole issue.