No. Even if you had an open sore where the water hit your mouth, the saliva will neutralize any bacterial threat in a few billionths of pathigen per thousandths of ml of water.
Germs are a real threat if you are not a generally healthy person. If you wash your hands frequently, you are less likely to catch illnesses. Worrying too much and causing stress can have its own ill effects on your health. Find a way to turn loose of your fear of germs.