Dogs don't get colds like humans, but they can develop upper respiratory illnesses such as kennel cough and canine influenza as well as bronchitis and inhaled allergies. You can read about bronchitis here:
It’s possible that sneezing and nasal congestion can be due to an allergic reaction to an inhaled substance. If this is the case, Benadryl can be given to your dog, the dose is up to 2mg per pound every 8 hours.
You can read about these here.
Kennel cough is normally contracted when a dog has been boarded or kenneled or around a large number of dogs such as at a dog show, dog park or pet store. Here is a website with more information on kennel cough. http://www.thepetcenter.com/gen/kenc.html
Canine influenza is now becoming more prevalent and like it sounds it is a canine flu. Here is an excellent site on it.
You will want to monitor your dogs condition looking for colored discharge from the nose or eyes, a productive cough (coughs stuff up), stops eating or lethargy. These are signs of a possible bacterial infection as well and my require antibiotics. If your dog appears to be having a difficult time breathing, you will need to see your Vet as some dogs dog get really sick with canine influenza and need support to recover.
To help your dog breathe easier you can run a NON-medicated humidifier in the room your dog is in, or sit in a steamed up bathroom with your dog to help keep the mucous moving. Robitussin DM at a 1/4 teaspoon per 5 pounds can be used to control the cough. Dosages can be obtained at this website. http://www.petplace.com/drug-library/dextromethorphan-robitussin-dm/page1.aspx
If your dog has not had all its vaccinations I urge you to have your dog seen as soon as possible.
There are other reasons for coughs such as heart problems which should be investigated if your dog is not on heartworm preventative or is an older dog. The following site goes over canine coughs.
Your dog could be doing what is called a reverse sneeze or a collapsing trachea. Here is a site on reverse sneezes and one on collapsing tracheas.
It sounds like your dog is coughing up some mucous and does need to see your vet so antibiotics can be prescribed. I hope you find this information helpful.