Welcome to the forum but I’m sorry it’s under these circumstances.
Has your vet told you anything more about the results of the blood tests, other than the elevated WBC? Have they told you what condition they’re treating with the antibiotics? I’m certainly not an avian health professional but antibiotics are ok for treating a bacterial infection but not much else as far as I understand.
Heavy metal poisoning is also perhaps something you could ask your vet to test for. Hopefully your birds don’t have one of those snuggle hut things that seem to be so popular as birds chewing on them can cause gastrointestinal blockages that can be fatal. Unfortunately the symptoms you’ve described are not an indication of any particular condition so it’s difficult to say what the actual problem might be.
I hope some other members may have some better insight for you and that your birdie makes a full recovery soon, it’s so worrying having a sick little one and not knowing why!