Upvote:4
It is often a good idea to apply for a visa if you've been refused entry (however, there's no guarantee the visa will be approved, and the 87-pound fee is nonrefundable)
However, you definitely can get in without a visa as well, if first getting yourself a new job (you should do this in advance even if applying for a visa. I'll stress this - hold off your visit until securing a job) and preparing all documentation proving ties to the US and that you won't overstay, work, claim public funds or make the UK your de facto home.
Please upload your refusal letter on here (with your personal details blacked out) so we know exactly what they got you on.
In general, though, you should at least bring any applicable documentation listed here (in "WHAT WE DID") and here (in "DOCUMENTS I CARRIED ALONG"), including but absolutely not limited to bank statements, a return flight confirmation and all relevant phone numbers (and make sure those people are available at any time)
Then be prepared for secondary inspection, and, most importantly, answer any and all questions confidently and truthfully (even personal and invasive ones), not least about whether you've had any past immigration issues (at passport control the officer will see a stop flag, which they will check, but they cannot see at first what it's about)
Additionally, you should shorten down your visit to max 1 month, and spend no more than 3 months in a year (not an actual rule, but my advice based on my own gut feeling), given that you lack a full-time job.
Finally, especially if your boyfriend has stronger ties to the UK than you do to the US, you should consider for him to visit you in the US instead, if at all possible.