Kiah, I'm sorry that your question wasn't answered in a timely manner. We don't have many avian vets on this site. It's important to note that once a conure acts ill it's already quite ill and in need of the attention of an avian-oriented vet and so I'm pleased to hear that your conure will be attended to shortly.. This is a protective mechanism because sick birds are attacked by other birds in the wild and within their flock. Droopy wings, head bobbing, lethargy, and wing flicking are important symptoms of but they're not pathognomonic (specifically indicative) of any one particular disorder. They do suggest weakness and perhaps respiratory disease.
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 your conure's choana - the slit between his oral cavity and nose - and cloaca (vent) may be taken. Whole body X-rays can be quite helpful as well.
Until your bird can be attended to, please heat up its environment to 29.4C by means of a 100W bulb shined into its partially covered cage (not at night when it needs to rest) or by taping a heating pad set on its lowest setting to the sides of its cage. It appears weakened and remove its perches and put its food and water on the bottom of the cage along with it. Add a water soluble avian vitamin such as Oasis brand to its water at half of the recommended dose so as not to make its water distasteful. Add a calcium supplement such as Calcivet or Calciboost to its water. These supplements are available in pet/feed stores. Avoid over the counter antibiotics designed to be placed in its 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 its diet consisted of, please? Seeds should compose less than 20% of its diet. A diet of mainly seed and nuts has excessive fat, carbohydrates, and phosphorus; marginal protein; adequate vitamin E, and are deficient in amino acids, calcium, available phosphorus, sodium, manganese, zinc, iron, vitamins A, D3 (necessary for efficient absorption of calcium), K, and B12, riboflavin, pantothenic acid, choline, and available niacin. 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.