I'm sorry to hear about this with Snowdrop. Her tail bobbing up and down in an exaggerated movement can indicate not only respiratory disease in the form of tracheal obstruction, pulmonary disease, or severe air sac disease but also external pressure on the air sacs due to internal organ enlargement/tumor, egg binding, or ascites (free fluid in the coelom/"abdomen"). It's important to note that once a budgie acts ill it's already quite ill and in need of the attention of an avian-oriented vet (please see here: www.theparrotsocietyuk.org/veterinaryadvice/avian-vets). This is a protective mechanism because sick birds are attacked by other birds in the wild. Her luffing (an attempt to conserve heat) and vocalizing are additional worrisome signs.
Until Snowdrop can be attended to, please heat up her environment to 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. If she appears weakened, 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 Vita-Drops 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 Snowdrop's diet consisted of, please? Seeds should comprise less than 20% of her 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 - yes, these low lactose foods are safe, 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.