Upvote:1
The Consultate General of Jamaica in New York lists what is needed, which does include a round trip or return ticket:
Requirements For Entry Into Jamaica
All visitors are required to be in possession of a national passport or other acceptable travel document establishing nationality and identity, and bearing a photograph. The passport or other travel document must be valid for the period of intended stay in the island. Visitors are also required to show evidence of sufficient funds to support themselves during their stay and be in possession of a return or round trip ticket to another country to which they are admissible.
Online relationships can be considered an issue, when you have never met those individuals in person. Should that arrangement fail, your ability to finance your stay might be questioned. Additionally, visiting an inmate requires prior application and approval by the Correctional authorities; had you done that?
All in all, it seems that a number of elements fell short, and you would want to take care of all of those before trying again with a round-trip ticket in hand.