I own a condo in Miami, Florida. Part of the ceiling and a wall have water damage. I had an A/C technician come to take a look at it because I thought it may have had something to do with the vent. He told me that it wasn't the air conditioner or the vents, but probably a drain leaking from the upstairs. I contacted the management company and they told me it is not their problem, but a problem between me and the owner of the apartment above mine.

Should I call a plumber myself?
Should I contact the owner of the apartment directly above me? (I've been trying, but no one has answered so far)
If I can't get in touch with the upstairs landlord, then should I pay for the repair?
Ultimately, who is liable for the damage and the repair?

Please help. Any advise would be appreciated.

Call your insurance co. Your condo owner's insurance should pay for all repairs and then they'll go after the person upstairs.