While Joy is right in that Zyrtec can cause drowsiness in a small percentage of users, it's also true that only 1% of Zyrtec users studied discontinued using it because of this. So, it seems that the drowsy effect is not all that severe or limiting.
Also, speaking from my personal experience, none of the second-generation antihistamines, including Allegra, Zyrtec, and Claritin, have significant drowsiness side effects, even though they warn of the possibility.
But your experience may be different.
To your health,
Not really. Zyrtec is an antihistamine, a class of drugs notorious for making people drowsy. But, it's a second-generation antihistamine, so it's less likely to make you drowsy than an older anthihistamine, such as Benadryl.
Still, drowsiness, tiredness and dry mouth are all possible side effects of Zyrtec.