and is there anyway to extend the period I can stay without getting a green card?
You can't extend the period without coming back to the UK and applying for a visa to move to the US. If you don't leave before the 90 days are up, you will become an illegal overstayer in the US.
Work visas are difficult to get (only 65,000 are issued every year to the entire world), so your best bet would probably be a student visa. Tuition in the US is expensive though and you would need to prove you had the money to cover the entire degree before you get the visa (a bachelors is 4 years, a masters is 2 years and a PhD can take anywhere from 4-10 years).
Say you studied at the University of Miami, if you were going for an undergraduate degree you would be looking at needing tuition fees of about $40,000 per year ($20,000 per semester), plus about $10,000 per year for living costs. If you were to do a masters, your tuition would probably be at least $30,000 per year (it depends how many lecture courses you sign up for each semester - as an international student, in order to keep the student visa valid, an undergrad must sign up to a minimum of 12 credit hours per semester, and a postgraduate 6 credit hours).
When I was 12, I visited my aunt in the US for the summer - I loved it so much that I decided I wanted to live there. It took me 10 years and two UK masters degrees before I got the opportunity to move there for an extended period of time (more than a few months)... I was accepted to study for a PhD in the US on a visa valid for 4 years.
So, I've now lived in the US twice on student visas - the first time was a study abroad year with my UK university in 2003 - I just had to pay half-fees to my UK uni (which worked out at only £500 for the year back then) and then living costs in the US (about $6,000 for the year).
The second time, I went back for the PhD - luckily my funding was provided by the university: I was paid $12,000 per year as a TA (Teaching Assistant), but I had to work 20 hours per week, teaching undergraduate labs, on top of my own lectures and research. The university also paid my tuition for me as part of the funding. Without the funding though, I could never have afforded to study for my PhD there.
As it was though, I moved back to the UK after 8 months... I wasn't enjoying my research, I missed my family, friends and English food/drink/TV/shops... and it got to the point that I just couldn't stand living there any more. Although I love to visit (I've been back 3 times since), I have no plans to live in the US again in the future.