Did you actually take your bird to your avian vet or did you just speak to them over the phone? I'm asking because typically they'll be able to show you how to syringe feed them properly, it's much easier if an experienced person shows you, but we can try. What are you feeding him? Formula, or did the vet give you supplemental nutrition?
It's much easier if you're using an oral syringe that has a longer tip on it. For the medication I'd try mixing it with a small amount of fruit juice. Baytril tastes horrible, so he's much more likely to swallow it if it's mixed with juice. Obviously you don't want to use a lot of juice because you want him to get all of the medication. Give him a syringe full of just the juice so he'll see that it's good, maybe even two, then give him the medicated juice. He'll just automatically swallow it down thinking that it's more yummy juice. Usually works really well, my birds absolutely love orange juice with no pulp.
As far as actually syringe feeding him, it depends on what it is you're feeding him and what you're using to feed him with.
Oh, always try to put the syringe in on the left side of his beak (your right looking at him), aiming diagonally across his mouth, over his tongue, towards the right side of the back of his throat with the tip of the syringe. That's where his crop entrance is, so if you aim the juice that way more of it should go into his crop, and you won't accidentally aspirate any. Definitely do this approach when feeding actual formula.
I'm concerned because I have never successfully gotten an adult bird to take food from a syringe, so I hope you are also providing solid food in case he feels up to eating it. Did they give subcutaneous fluids to help him perk up? I have a video which I will try to link below that is just a simple demonstration of me administering baytril (which my phone just autocorrected to nautilus of all things) to a bird who doesn't want it, just in case your vet didn't demonstrate, although they really should have. The key thing is GO SLOWLY! You can't really go too slow, but you CAN go too fast and aspirated your bird so please be extremely careful.
If you find you aren't able to get the food or meds or fluid into your bird, ask the vet if the bird can stay in their care until he is a bit more stable. If they don't do medical boarding, ask if they know who does.
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Cockatiels:Battle, Sniper, Jackie, Honi
Blue Headed Pionus: Mel
Green Cheeked Conures: Flick, Cache, Titan
Indian Ringeck Parakeets: Blue, Kamehameha, Ka'iulani, Kahili, Shadow, Ali'i, Noni, Pono, Smokey, Hapu'u
Yes, we went to the vet. But I didn't ask how so I guess they assumed I was ok.
The supplement is a powder mix. I can try the juice but the problem seems to be he is refusing to swallow anything. However, he ate a few seeds on his own, but only a few. I'm so worried, he's mostly inactive and stumbles when he tries to move.
Its only been a few hours with the medicine but as I said, I'm not sure how much I actually got him to swallow.
Oh wow, I'm so so sorry, what a horrible thing. It's not anything you did and it wasn't because he hadn't eaten in a day either, he must have had the infection for quite awhile and he was septic. It's so hard to tell that they are sick, they do such a good job at hiding illnesses that by the time you realize they are ill it's just too late to treat them. You did the right thing, you took him to the vet when you knew he was sick.
I am so sorry you just had to go through this, we've all been there and know how hard it is. He died in your arms, knowing that he was loved.