I am sorry no one has responded to your post.
There is a specific permit to intent to marry/cohabinating. It´s called a resident permit.
You get it through the Swedish Embassy in Washington DC.
You need to schedule with them for a meeting to get the paper work started. It is supposed to take 2-3 months to get your permit.
Before you go to the Embassy you need to have with you a filled in form called "invitation letter" from your partner. He/she downloads it from the Swedish immigration site, fills it in, send it to you and you bring it with you to the embassy. No permit process will start without this piece of paper.
Me and my fiancé are about to start this process, sadly the line is long to get a meeting in the embassy (two months wait). Hopefully they do not have much to do so the permit process is faster than usual.
Best of wishes