I'm sorry to hear about this with Rio.
The complex anatomy of the infraorbital sinuses and diverticula of birds lends itself to the establishment and persistence of upper respiratory tract infections. When combined with factors such as hypovitaminosis A - a lack of vitamin A in the diet (causing pathologic changes in the lining of the sinuses and decreased normal function and resistance to infection), irritation of the sinus linings (e.g., ammonia toxicosis in poorly ventilated, unhygienic cages and aviaries), cigarette smoke, or other aerosol pollutants), extremes of humidity (too dry, too moist), it's little wonder that such infections are common in birds.
Infectious agents are usually secondary invaders taking advantage of the conditions described above. They include bacteria, viruses, fungi, and even parasites. Rio will require the services of an avian vet (theparrotsocietyuk.org/veterinaryadvice/avian-vets) who will attempt to clarify which type of infection is present and then treat specifically. It's important to recognize that once a budgie acts ill it's already quite ill.
Until Reo can be attended to, please heat up his environment to 29.4C by means of a 100W bulb shined into his partially covered cage (not at night when he needs to rest) or by taping a heating pad set on its lowest setting to the sides of his cage. If he appears weakened, remove his perches and put his food and water on the bottom of the cage along with him. Add a water-soluble avian vitamin such as Oasis brand Vita-Drops 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/feed 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.
Nutritional imbalances are a common cause of illness in our pet birds. What has Rio's diet consisted of, please? Seeds should comprise 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 - 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. Here are some tricks in transitioning Rio to pellets: https://www.harrisonsbirdfoods.com/using-our-foods/diet-conversion/
Please respond with further questions or concerns if you wish.