Yep, Gwen's right. You used to be able to do this - some of us got married on tourist visas and switched to FLR whilst in country - but that was years ago. I think it changed in 2003. At any rate, it's definitely changed and you'll have to go back to the US and apply for a student visa from there. You can do it in person same day at a British Embassy, but it's not cheap.
I would also think long and hard about studying here to live with a boyfriend w/whom your future is uncertain. Fair play if it was always your dream to study here, but it is a very, very costly - for you, at any rate - way to test out a relationship b/c of international student fees.