Chicken soup is great for influenza because it is a salty liquid and salty liquids are exactly what you need when you have flu. It won't help in this situation as far as I know.
A Neti pot is great, but you apparently don't have one so you can also use saline nasal spray if you have that on hand. A word of warning to everyone -- I had a torn retina a couple years ago. Fortunately the Dr. fixed it 100%. BUT -- he photographed my retinas and told me to stop using nasal decongestant spray. He showed me the damage on my retinas from using nasal spray. I've used saline spray instead ever since.
Hot mint tea would also open things up and make them drain faster. Sounds counter-intuitive but unless you're making more fluids at a faster rate, the faster you drain your sinuses the sooner they'll stop draining if that makes sense.
One of the best things for a blocked nose is to hold a teaspoon of horseradish in your mouth for a minute. The fumes etc really open up those passages. Again, sounds counter intuitive but if the posterior nasal passage open you might convert a runny nose to post nasal drip which is preferable in my opinion.
That's all I got.