I took Alka Seltzer Plus earlier, and I want to know if I could take NyQuil before I go to sleep?

Depends. I would wait at least 4 hours between the two.Some on the ingredients can interact but should not cause any problems in normal dosage but best to wait.
What for? What are you taking these medications for? What else are you taking? Make sure that the total dose o acetaminophen in the various medications does not exceed 4 gm/day. Most of the medications of the kind you are taking may provide symptomatic relief but do not address underlying issues. If your symptoms persist, it would be prudent to see your doctor.