Generally no — Zyrtec (cetirizine) and Claritin (loratadine) are both non-drowsy antihistamines of the same type, and the NHS says not to take two antihistamines together unless a doctor tells you to.
Zyrtec (cetirizine) and Claritin (loratadine) are both second-generation, "non-drowsy" oral antihistamines that work the same way — by blocking H1 histamine receptors — so taking them together generally adds no extra allergy relief, just a higher chance of side effects. The NHS states plainly on both drug pages: "Do not take 2 antihistamines together unless recommended by your doctor." The only routine exception it describes is a doctor advising a daytime non-drowsy antihistamine plus a separate sedating (drowsy) antihistamine at night for a few days to control a severe, itchy skin rash — not doubling up on two non-drowsy ones like these. If your allergy symptoms aren't controlled on one, the better move is to ask a pharmacist about switching products or adding a different type of treatment, not stacking two of the same class.
Pick one of the two and take it at its labeled once-daily dose rather than both. If one isn't working well enough, the NHS notes the other non-drowsy antihistamines (loratadine, cetirizine, fexofenadine, levocetirizine) "seem to work as well," so try switching rather than combining, and ask a pharmacist about safe add-ons like a steroid nasal spray or antihistamine eye drops, which the NHS says are fine to use alongside a single oral antihistamine. Only take two antihistamines at once if a doctor has specifically directed it (for example, a non-drowsy one by day and a sedating one at night for a severe itchy rash). Watch for additive side effects such as drowsiness, dry mouth, headache, or trouble passing urine — and drowsiness in particular is more likely if you also drink alcohol or take other medicines that cause sleepiness. Speak to a pharmacist or doctor before combining if you're on other medications, are pregnant or breastfeeding, are giving these to a child, or have kidney or liver problems, and call a professional (or Poison Control at 1-800-222-1222 in the US) if you accidentally take too much.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.