As a U.S. citizen living in a U.S. territory, it does get a little tricky. Since your employer is SC based, you will need to file a U.S. income tax return unless they claim all income is earned in Puerto Rico and you are a bona fide resident -then you only need to file the PR return. See Topic 901
Which means for now, a US return is required. If the employer treats you as working in MA, where you feel to be a resident with intentions to return and make that your home base again, then you could go that route.
As for residency, you aren't trying to become a US citizen so the residency issue consists of tax home, physical presence and the closeness connection. While you feel closely connected to MA now, I would imagine that moving to be with a new partner implies that you plan on making a new life there. You may be testing the waters for now but should revisit the thought process and your plans every so often.
We do not handle PR tax so I can't speak to those issues. You will need to make some decisions and decide if /when you want to declare a residency there. If you need to file, you can file the Puerto Rico state return directly with the Commonwealth of Puerto Rico.
For more information see IRS Publication 570 page 14.
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