Birds hide illnesses extremely well. Unless you carefully watch for signs(such as absorbing droppings daily, checking nares and eyes, and watching for any odd behavior, becoming knowledgeable on several bird illnesses, etc) you might not know your bird is sick until it starts showing symptoms like fluffing up and acting lethargic. At this point they are really badly sick.
Your bird 'might' have an infection. You can try and treat it holistically but then you dont know what kind of infection it is or if its an infection at all. Only a vet can give you a diagnoses. I would suggest putting some turmeric powder and cinnamon powder into the fresh food or in the water. Only add about a pinch and do this 3-4 times a week. Turmeric and cinnamon are both known for their antiviral, antifungal, antibacterial properties so they should help a bit.
When looking for a vet always check their reviews, whether they are on yelp or some other website. To be honest, the vet should not have put down your cat without consulting you about any other options to save her/him. I had a cat who ingested poison and after the vet determined what was wrong with him they asked if we would like to pursue treatment or put him to sleep. My cat was missing for 2 days and came home vomiting blood on the third day, he lost a ton of blood and was suffering, on top of that the vet said in his condition there was a little to no chance he would survive. So we decided to do what was best and put him out of his suffering.
If you take your bird to the vet make sure the vet is avian certified and also has a lot of experience. Ask them how many bird patients they have. A bird hospital would be most suitable as I find that mixed animal vets dont know very much about avians.
Thanks for the advice but she is so much better no longer huddled up and puffy she is active playful and enjoys her new mate