I'm sorry to hear of this, Dorothy. It's important to recognize that a vitamin A deficiency can represent as respiratory infection or the two problems can co-exist. Bonnie may be eating to excess in an attempt to replace the nutrtients he lacks. Diabetes melllitus is another consideration but unlikely in a 3 year old budgie.
What has Bonnie's diet consisted of, please? Seeds should compose less than 20% of his 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.
For now, add a water soluble avian vitamin such as Oasis brand to his water at half of the recommended dose so as not to make his water distasteful. Add a calcium supplement such as Calcivet or Calciboost to his water. These supplements are available in pet/agricultural merchant stores. Avoid over the counter antibiotics designed to be placed in his water. They won't be effective if only because an ill bird won't drink enough to medicate itself properly. Please respond with further questions or concerns if you wish.