Can I take nyquil at night when I'm also taking Claritin (loratadine) and atarax?

Claritin (loratadine) Not Atarax. You may combine nyquil & claritin (loratadine). The latter is a non-sedating antihistamine. Nyquil contains a sedating antihistamine & Atarax is another. Liquid formulations of nyquil contain a lot of alcohol. So if a drunken stupor is your goal you'll achieve it with nyquil & atarax. There are better & safer ways to treat your allergies. Skin testing is more cost-effective than immunocap & equally accurate.
Duplicate therapy. Nyquil and Atarax (hydroxyzine) are quite close caution advised is advised as the combination may increase the risk of CNS depression, anticholinergic and other adverse effects. I would advise allergy testing (immunecap blood test specific for your area) to see if you really need that much allergy medicine or if you need to gear treatment more towards your symptoms.