British citizenship status - Barbados

Hello, Can anyone help to say whether I still need to register or naturalise or not?

-44 years in UK (arrived from Barbados 1973 age 20),
-father had British passport before Barbados independence 1966 (he moved to uk 1953),
-my passport is Barbadian and the original one states "moved to UK to be with parents",
-40 year relationship with British citizen but never married (one uk born daughter),
-never been out of the country (always employed here) untill 2 months ago for holiday to Barbados whereupon my return to uk I was challenged and now have 6 month visa only

Very anxious

You arrived in 1973- but on what basis were you admitted by the United Kingdom. Were you granted an immigrant/settlement entry clearance in your Barbados passport?

People from colonies generally lost British nationality on independence (Barbados- in 1966) unless they had certain ties through birth or (paternal line) descent with the United Kingdom or a place that remained a colony. This included persons living in the United Kingdom- such as your father- if they became Barbados citizens at independence. Unless your father's own father or his paternal grandfather was born or naturalised anywhere else in the U.K./Colonies?

It's near-certain you need an immigration solicitor straight away but the first step should be to clarify what was your original immigration status?