Alarm's set but icon in the right corner not showing on my iPhone

You do not say what phone you have. Alarm symbol will show there on iPhone 8 or older. For newer phones (with the notch) you need to drag down from top RH corner to see Control Panel, same as you need for showing battery % charge, headphone symbol etc.

iphone 12 does not show alarm symbol on the main screen you have to use control center