I'm sorry that your question wasn't answered in a timely manner. It's important to note that once an African Grey acts ill they're often quite ill and in need of the attention of an avian-oriented vet (please see here: www.aav.org). I understand the logistical constraint you're likely to have where you live, however. This is a protective mechanism because sick birds are attacked by other birds in the wild. Smokey's "cold" symptoms and are important symptoms but they're not pathognomonic (specifically indicative) of any one specific infection and might involve a vitamin A deficiency as well. I don't know if Smokey is a he or she and so I'll refer to Smokey as a she in this discussion.
An avian-oriented vet might first treat symptomatically and supportively by providing supplemental fluids and electrolytes by needle and tube feeding a "recovery" food. Blood tests and cultures of Smokey's choana - the slit between her oral cavity and nose - and cloaca (vent) may be taken.
Until Smokey can be attended to, please heat up her environment to 85F (29.4C) by means of a 100W bulb shined into her partially covered cage (not at night when she needs to rest) or by taping a heating pad set on its lowest setting to the sides of her cage. Remove her perches and put her food and water on the bottom of the cage along with her. Add a water soluble avian vitamin such as Oasis brand to her water at half of the recommended dose so as not to make her water distasteful. Add a calcium supplement such as Calcivet or Calciboost to her water. These supplements are available in pet/feed stores. Avoid over the counter antibiotics designed to be placed in her water. They won't be effective if only because an ill bird won't drink enough to medicate itself properly.
Nutritional imbalances are a common cause of illness in our pet birds. What has Smokey's diet consisted of, please? Seeds should compose less than 20% of her diet. Ideally, a balanced pelleted diet such as can be found here: www.harrisonsbirdfoods.com or here: www.lafeber.com/pet-birds should be fed as well as hard boiled egg yolk, pancakes and cornbread, the tops of fresh greens, dairy products such as yogurt and cheese, fresh fruits such as apples, pears, melon, kiwi, and berries, vegetables such as broccoli, carrots, beets, asparagus, cabbage, sweet potato, and squash, and even tiny pieces of meat.
Please respond with further questions or concerns if you wish.