The University of the Caribbean offered me admission in Communication. I want to know if its an accredited online institution

There are many websites in Google that explain what this university offers in the caribbean. While you look them over you can, in fact, e mail them for information to be sent to you. I see no reason to doubt them as an accredited university.

Tick

Accredited how ?

in their nation, in England, in the US ?

If you are talking about accredited by the US Dept of Education, then you go to the Dept of Education web site and they list all accedited colleges that they do

There are 1000's of agencies that accredit, some have great value, some have no value.