Okay. First things first, it is extremely difficult to move to England for a longish period of time (more than 6 months.) Options include a student visa if you want to go to grad school, a work visa if you happened to be trained in a shortage area (such as nursing, social work or teaching) or you were transferred to the UK by an American company (if you don't fit into either one of those two categories, getting a work permit is pretty much impossible.) There's also the Highly Skilled Migrant Program, but you have to have a few years of full time work experience at a graduate level before you can qualify for that. And finally there's marriage to a Brit. That's the simplest and easiest way to move to the UK, so really think about it if it's at all an option for you and your boyfriend- many people have no other options to be with their SO besides marriage. It sucks if you're not ready to get married yet, but that's just the way it is. And by the way, the UK fiancee visa allows 6 months for marriage, not 3- it's the US fiance visa that stipulates marriage within 90 days.
Now, you're a student, which means you can get a BUNAC visa to the UK after you graduate. The BUNAC permit allows you to work, but it only lasts for 6 months. You also have to enter the UK within six months of being in school- so since you're graduating this spring you have until December 31 to enter the UK with BUNAC or else you're not eligible. If you have any claim of EU or Commonwealth citizenship, that'll also give you more options, but otherwise, BUNAC for 6 months, student visa, fiancee/marriage visa, or coming over as a visitor (not allowed to work) are pretty much your options.
Hope this helps!