Working in the ER during flu season, I have to say that MAYBE 50% of my patients who present with flu like symptoms actually have the flu. While it's highly unlikely (nothing's impossible) you'll give it to your animals, if you're one of the 50% who has something else, that COULD be transmitted.
Still, it shouldn't be an issue since you're washing and sanitizing your hands.
You ARE keeping your hands clean, right?
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