CGCampbell has provided a good answer. It is likely that you will not be granted a Schengen visa (that is what you are applying for, there's no Swedish visa) because your situation is precisely the one where governments often deny visas - you are from a less developed country, cannot show a source of income, and cannot show strong ties to your home country.
If you are traveling to Sweden on a visa, you are generally required to show at least 450 SEK (about 60 USD) for each day you will be staying in the country. That from the Swedish Migration Board. It also says it's possible to travel with a lower amount of money if someone will be providing for your needs.
There is one possibility for you, which is that your boyfriend completes and provides an invitation to Sweden on your behalf. It's described on this page, still in Swedish, but you can see the form. Scroll down to where it says Blanketter, and the second link shows the invitation form in English. Here's the page in English, it says the same thing as in Swedish. The procedure is such: the person in Sweden (your boyfriend) completes the form and sends it along with the necessary documentation to you. You then enclose all of that with your visa application at the Swedish consulate or embassy.
In the case of an invitation, your boyfriend would be required to guarantee that he is paying for your stay, and also show sufficient income. His legal status in Sweden, which you have not provided in your question, is critical here. If he's not a resident of Sweden, it will essentially be impossible for him to send an invitation (it doesn't say so directly anywhere, but the form requires a personal identity number, which only residents have, and it wouldn't be possible to get the other required documents from the tax agency without being a resident). If he is a resident of Sweden, and provably has enough money (which means he has a job or can show a bank statement with a fairly significant sum of money), then it might help you.
If your boyfriend cannot provide such an invitation for financial or residency reasons, it is extremely unlikely you would be granted a visa from a repeat application or appeal. If such an invitation can be provided, it still does not guarantee you a visa because there is no strong proof, given what you described, of you intending to leave the Schengen area.
UPDATE given the edit
Your boyfriend being a Swedish citizen is good news for your visa. The fact that he already sent the invitation and stated he'd support you is bad news - if they rejected your application with his invitation, there is very little you could add to improve your chances.
Unfortunately for you, the extra documentation you list for your planned appeal is not all that helpful. Letters from your parents will have no influence whatsoever on the decision, let alone letters from neighbours. Neighbours will not count as "social ties" under any conceivable scenario, and at best such letters will give your case officer a laugh.
Receipts from your business are not particularly helpful because it's a small amount of money (from what you've indicated), and is an online business anyway - it's not a job in Kenya, there's no need for you to return to Kenya to continue with it.
The M-Pesa system papers might be slightly helpful if you can show you have a s significant amount of money in your account. If it reaches the recommended value of 450 SEK per day of your stay in Sweden, that is good.
One extra university course might not be particularly helpful here, unless you can clearly show that you will be graduating after your return from Sweden, and not before.
Hopefully your new apartment lease is sufficiently long. It should probably be at least for a year to indicate a commitment.
One thing that could help you somewhat is to buy a return flight from Sweden to Kenya, and show it with your application. Yes, it will be a waste of money if you're still not granted a visa, but to be honest, your application seems pretty weak so you might want to do everything to make it look better.
From the Swedish government's perspective, I think the same problem will remain. The fact that you have a boyfriend in Sweden makes it seem possible that you would want to move there permanently (in which case you need a completely different visa and process). Normally you prove that your visit will be temporarily by showing ties to and commitments in your home country. Yours are, even with the update information, strenuous at best. That is the main problem with your application (not the finances), and that remains a problem even with the extra documentation you mention.