I'm very sorry that your baby is so sick. Ginger had a good idea about asking your vet if he could call an avian vet for a consultation. Also, you do need to get food into him. He needs the fuel to keep fighting the illness. In order to perk him up so he will feel more like eating, you could try putting a few drops of Karo syrup into water and feeding him with a syringe. The only possible downside to that, would be if he has a fungal or yeast infection the sugar gives it sustenance.
Can you look down his throat to see if he has any whitish spots? He's so tiny, but try to smell his breath - if it smell like garbage you are most likely (not for sure) looking at a yeast infection. Put a drop or two of apple cider vinegar in his water, which will help with a fungus or yeast.
Keep asking questions and updating us on his condition.
ML