IMO it shouldn't be on you to return to the airport to file a claim. The DL baggage agent should have done this upon arrival, and if she (?) didn't know how to do this, she should have immediately consulted a redcoat or called her help desk/supervisor.

I would also hope that any employee (airline, contract, airport, or TSA) would be severely disciplined for vomiting on a bag and not making any report or telling anyone that he/she was sick and should not be on duty. I can't imagine anyone not noticing this and assuming that the customer wouldn't notice either. In fact, I wonder whether biohazard exposure on the job is an OSHA issue that was required to have been reported.