Hi Arijor,
I've not yet done any research on Trinidadian East Indian heritage, so I do not know if you have to go back to get it done.
However, if you are tracing your heritage, all the rules still apply. You need to establish each link in your ancestral chain properly. If not, you might end up researching someone who had nothing at all to do with your family. So starting from yourself, work backward to establish each link - you to your parents to their parents to their parents. Given that the East Indian presence in Trinidad is fairly recent, you should hit upon the indentureship period fairly quickly.
I know that the National Archives of Trinidad and Tobago (NATT) has the actual record books documenting the arrival of East Indians there. They were on display for the 2012 Indian Arrival day celebrations. I cannot say if they are available elsewhere. You should probably contact the NATT and ask what records are available for East Indian genealogical research. I'm sure they will be willing to tell you. You can check their Facebook page for more information:
[https://www.facebook.com/pages/National-Archives-of-Trinidad...]

Hope this helps....