Depending on which version of Nyquil you take you get:
An analgesic (pain reliever, usually acetaminophen [common brand: Tylenol], which one needs to be careful with, since taking more than recommended can damage the liver, so, don't take Tylenol in addition to Nyquil)
A cough suppressant: dextromethorphan, whose effectiveness is doubtful
An antihistamine: Doxylamine, which is what is likely drying you out as it tamps down the body's overreaction to a cold. It's also what makes one drowsy so that Nyquil can market itself as 'helps you get to sleep' medicine.
I don't like combination drugs since you can't fine-tune what you need.
I keep these handy:
Four analgesics: aspirin, ibuprofen [Advil], acetaminophen [Tylenol], and naproxen [Aleve]. Usually in liquid gel form for quicker uptake. I rotate using them to avoid any rebound effect or building up a tolerance. The last two can be dangerous if you take more than the recommended dosage.
Antihistamine: Chlorpheniramine [ChlorTrimeton]. It causes the least drowsiness of the first generation antihistamines.
Caffeine pills: I don't drink coffee. Caffeine counteracts the drowsiness of the antihistamine. It is also, by itself, a recommended OTC medication for migraines (which I get). Excedrin, e.g., is aspirin plus caffeine. And marketing of marketing, "Exedrin PM" which "helps you sleep" is Excedrin without the caffeine, IOW, it's just plain aspirin and has no sleep-inducing benefits. Caffeine pills also help if your headache is from caffeine withdrawal.
Pseudoephedrine: AKA, Sudafed. This is heavily regulated in the U.S. because in large quantities, it can be used to create Meth. So, you may have to show ID at a pharmacy to buy it. But, it is definitely a very very effective decongestant that can temporarily open up nasal passages and stop runny noses.
A nasal decongestant: Usually Neo-Synephrine for short bursts of clear nose and stopping the nose from running for when I absolutely have to work or be about (e.g., go to the store) so that I'm not constantly blowing my nose.
Visine-A: Visine with chlorphenarimine in it. Guaranteed (for me) to stop itching, running, dry, or red eyes.
By keeping ones medications separated, you can use the right drug for the right purpose at the right time in the right dosage. E.g., to get to sleep while I have a cold, the decongestant allows for easy breathing, and the antihistamine's drowsiness is a plus.
For me, caffeine+antihistamine+analgesic can shut down an oncoming migraine (with Naproxen being the most effective analgesic). And if it's really bad, a second dose with a different analgesic is almost always a guaranteed solution.
But, before using any of these suggested meds, read their Wiki page info and the counterindications on the packaging for side effects, situations to avoid mixing drugs, and health conditions that would prevent you from taking these meds. Consult a doctor.