I took 2 benzonatate capsules at 8am for my cough. It's now 8pm. Is it okay for me to take DayQuil? I'd prefer to take it.

Yes. There is no problem with the combination. Whether they work or not is another issue.
Benzonatate and. Dayquil use different medications to help with coughing, so you should be able to do that without a problem. You are welcome to try other over the counter formulations which would be the same as Dayquil, but no more than 1 dose every 8 hours. Thanks for trusting in HealthTap.