It takes patience and practice. I think the half notes are the pons asinorum of tin whistle playing. I find it easiest to cover the side. Which side depends on the hand - assuming left hand on top then I would cover the top 3 on the left side (i.e. the side the finger naturally covers) and vice versa for the bottom. While it takes some practice this allows you to develop a faster fingering technique in the long term and play better ornamentation. The shrill sound will disappear with practice. Best wishes GB