This is very normal for beginners.
Breathing from your chest could be the cause. Many students get light headed in the beginning. It usually gets better over time.
You may need try breathing from your diaphragm. What’s probably happening is that you are super oxygenating your blood, which is generally considered extremely health in reasonable doses.
I actually enjoy that light-headed feeling to a certain degree and consider it extremely healthy, as it indicates super-oxygenation of the blood and tends to increase my feeling of vitality. The sensation generally passes within a few minutes of stopping and is nothing to worry about.
Playing the harmonica is all about breath management. The more you play, the better you'll get. Playing rhythms is a great exercise for the lungs, and they will help increase your lung capacity.