Can I take hydrocodone and a non-drowsy allergy medication?

Yes. Should be ok at normal doses of hydrocodone (5-15 mg per dose, 3-4 times a day). At VERY high doses (more than 120 mg per day), there is a slight risk of heart arrhythmia along with things like ephedrine (ephedrine sulfate) or psuedoephedrine (ephedrine sulfate) due to an additive effect.