Update: airberlin has said my bag made it to BUD on Sunday. They are going to ship it to my permanent address in New York.
The only reason I went to the baggage office in JFK was because the baggage claims desk in BUD had told me to do it. As per, they said it would somehow be there when I land. Second, to clear things up, BA scanned my claims tag (the little bit left after peeling away the baggage tag) in LHR because they thought it possibly might be on the flight anyway since the baggage desk in BUD had my connecting flight numbers. Of course, it wasn't and BA told me to talk to AB when I went to the baggage lost and found at JFK. There was a huge confusion on what happened at that moment.
I don't usually check my bag unless it's really heavy and fill with nothing necessary. The bag was filled with Swiss chocolate and other Swiss foods/snacks. I find it absolutely crazy an airline would let a plane depart without the passenger's luggage. A few people in the long line for the baggage desk claims were leaving within 24 hours on connecting flights.