You should hold on to your burning ambition to be famous one day, but you should also realize that it is an extreme long shot. There are so many wannabees, in theatre schools and out of them. Fame is largely a matter of luck as well as extreme talent, the right 'look', and being in the right place at the right time. And just achieving one of thosse simply isn't enough. You have to possess the lot. So that, if you even moved to Hollywood, you'd find endless people of talent working in bars and restaurants, for minimum pay, vainly hoping and praying for a big break.
When you say you have appeared in six plays, was that professionally or as an amateur?
At the very least you need to have gone, as an adult to the Royal Academy of Dramatic Art, to give you half a chance of succeeding on stage. There is little point, except for fun, in becoming a movie 'extra'. Extras are seldom to never even acknowledged except as a herd, but it could at least give you something to put on a CV (resume), when trying to compete for those scarce openings. And of course, the minute you can, you need to have an agent to promote you. An agent will take you on once you have had a couple of minor successes.