Looks like .5 to 1 cc is correct: https://www.backyardchickens.com/t/86782/tylan-injection-how-do-i-do-it
Sounded like a lot to me but apparently your calculation was correct, and overdosing on antibiotics is pretty unlikely.
I wouldn't worry about an overdose as long as you are close (most antibiotics aren't an overdose risk).
Half a cc orally? Injected? Mixed in water? I have never used Tylan. Like I said change the subject line to ask a direct question as others here will know the proper dose.
If it is oral I...
There must be a dosage chart somewhere on the site. If you can't find it see if you can edit the header of your original post and ask that direct question.
IMO the symptoms sound a lot like possible mycoplasma. https://poultrykeeper.com/respiratory-problems/mycoplasma/
Now I am sure someone will pop up and say kill every bird on your property, burn the coop down, salt the land etc... But don't over-react. Are most of the other birds healthy...