Sorry about your hen. Did you try to get the state vet to do a necropsy to find the cause of death? The body would need to be kept cool and taken in right away tomorrow, or shipped overnight on ice packs. Here is the list of state vents:
https://www.metzerfarms.com/PoultryLabs.cfm
Personally, I would not give Tramadol to a chicken. It is an opioid-like medication, and I would avoid it. Aspirin can be given, 81 mg twice a day, and some have used ibuprofen 5-10 mg 2-3 times daily, but do not use Tylenol.