What else should I have?
Evidence showing where you live in the US and where you'll be living when you return. It's probably best if that is the same place. It's also helpful if you own or lease the place yourself and have the documents to show it.
I’m worried I’ll be denied or detained because it’s for such a long time. Am I over reacting?
It's hard to say. If you're detained, at least, it will only be as long as is necessary to put you on a plane back to the US.
As you probably know, visitors to the UK are allowed to stay for as long as six months, so the duration of your stay is not inherently a problem. You could indeed have a problem convincing the immigration officer that you are a "genuine visitor."
Your circumstances include some red flags, so you are right to be concerned. Being a temporary worker could increase suspicion that you will seek freelance work in the UK. On the other hand, it makes your plan to spend three months in the UK more credible than it would be if you were a full-time long-term employee.
If your income is sufficient that you can forego it for three months comfortably, that will help, but given your mention of support from your father and that your boyfriend is a full-time professional, it seems that your income may not be that high.
Another thing you should be aware of is that the UK officers are supposed to make sure that any money you claim is legitimately yours to use. If you rely on your father's money, you should have a statement from him that he does not expect you to repay it. You should also be prepared to present his bank statements to show that he acquired the money legitimately.
If you have time before you travel, you may want to consider applying for a standard visitor visa, even though you are not required to have one. This would allow you to make your case in the privacy of your own home rather than in a busy airport immigration hall. Having the visa does not guarantee entry, but it does limit the degree to which the immigration officer will investigate you, since the visa shows that you have already been investigated. This approach should alleviate some of your anxiety.
If you do not have time to apply for the visa, you should nonetheless read the guidance and prepare the same documents that you would for an application. Bring them with you so you can show them to the immigration officer if necessary.
Finally, you probably should not volunteer them until it becomes apparent that the officer is concerned. You don't want to appear like you're hiding something. So be prepared to answer in detail, but don't offer the detail unless asked.