The backlog of current visa applications applicable to nursing goes back to 2006 - meaning those who had an application in with a processing date of 2006, are still waiting. The nurse specific H1-C visa was stopped around 2009 so that really leaves the H1-B visa (non-immigrant specialty occupation) as a possible option.
Problem being, the H1-B typically requires the applicant to have a degree specific to the occupation. Right now, there is no national mandate in the US to have a BSN in order to practice, so the USCIS (the ones who allocate visas) don't really see 'nursing' as fitting the H1-B criteria. Perhaps with certain speciality advanced practice RN positions, a remote location, and a good lawyer it would be a slim possibility, but it's not for the majority of general staff nurses looking to move. Additionally, there is a cap on the amount of H1-Bs given out per year (< 70,000) and about a third of these are allocated to IT professionals from the Indian sub continent, the day they become available.
Contacting the likes of the NREMT will only waste your time and money unless you already have an 'in' to the US. They cannot provide you with one.
It's not all doom and gloom though. Sweden is one of the countries eligible for the diversity visa lottery program, so you may wish to look at this.
http://travel.state.gov/visa/immigrants/types/types_1322.html
Also have a look at Canada. You could always visit the US.
Good luck.