I took the cough medication Hycodan (hydrocodone) at around 7pm. Its 10:30pm, would it be ok to take nyquil?

Cough control. Hycodan (hydrocodone) can give excellent relief of cough. Unfortunately, if you are coughing again a lot after 3-4 hours, I would say the Hycodan (hydrocodone) levels are not sufficient to relieve the cough by itself. Hopefully, taking the NyQuil at that point will hopefully give you additive benefit. I would not typically take both meds together. If your cough is increasing/getting worse, see your doctor.
Yes these medicines. have different ingredients and should not interact. Though Nyquil typically has an antihistamine that is designed to "dry" you up so you can breathe and sleep at night. The sleepy effect of the antihistamine may combine with the hydrocodone to give you more grogginess in the AM, so make sure you give yourself plenty of time to wake up and if you have to drive, I would not take the Nyquil.