I am taking Allegra (fexofenadine) D non drowsy but I've got a bad cold can I take NyQuil cold and flu with it?

Yes. You could take Allegra-D in the day then NyQuil at night. Hope you get better soon.
They are similar. NyQuil may make you drowsy. You neglect to itemize the details of your "bad cold". Are you taking any meds? The best approach can be determined only if the details are given.