Sorry to hear about Birdie not feeling well.
A few months ago we went through something similar with our cat, Shadow. He's almost 14, though. Vomiting, no appetite, lethargic, in pain. Turned out to be pancreatitis. Got so sick i was looking at urns online so I could send his ashes to my younger son. After about two weeks or so, he finally started to eat a little and seemed to be in less pain. Eventually he seemed to get almost completely back to normal, but now every once in a while he acts like it is coming back again, and has a day or two where he looks like he is going to go through the downward spiral again. Thankfully he hasn't.
Man, it's tough watching your pet suffer.