Loratadine makes me drowsy, should I try cetirizine to see if that doesn't do the same thing?

You can. Loratadine & Cetirizine are both in a class of medications known as non-drowsy long acting anti-histamines. Although they are in the same class, i still have patients that experience drowsiness (usually more from cetirizine); however, i would try it because everyone responds differently to the same medications. Take it before bed so if drowsy you can go to sleep anyway.
Fexofenadine less . Loratidine has 8% sedation and Cetirizine 13%, so the latter is not actually permitted by the fda to advertise that it is non-sedating. In practice, i agree, responses vary. Fexofenadine is less sedating (2%) than either, but some patients claim even it sedates. If the antihistamine is for nasal allergies, prescription topical antihistamines are less sedating than oral (but cost more).