I wouldn't advise that. They are both medicines with sleeping aids in them. Go out and buy some NyQuil, take the recommended dose (I think its 30mg) and be prepared to be sleepy within about 30 mins.
If possible, take the NyQuil and lay down - read a book or watch some TV. That way, you'll give your body a chance to relax and let the sleep agent do its job
Keep in mind, that your body can become dependent on NyQuil if you take it for more than a few days. I remember taking it for about a week, every night (I was desperate to get some sleep during withdrawal's). Then one night, I didn't take it - Holy crap, I didn't fall asleep until 7am!! So, just be careful.
I hope you get some sleep tonight