Would I be able to join and possibly change careers like you did?

If you have a British Passport you can join the British Army. Anyone serving can transfer into different capbadges throughout their career depending on a number of factors; recommendations (if req), quals (if required), spaces available in the trade you want to go into, your rank at the time of wanting to transfer etc etc. There's loads of different factors that could come into it at the time - and something you'd speak with your career manager about. I hope that helps for now.