Get your medical degree in Sweden. Then, if you still are interested in working in the US, you can take the foreign medical exams and apply for a medical residency in the US. That would bring you here for the length of time that the residency lasts. After completing your residency (or residencies if you want more than one specialization) there is a good chance that you could find a permanent job in the US. You might need to start out working in an underserved part of the US, but eventually you would be able to get your green card (legal permanent resident status) and then work anywhere in the US that you choose.
Many, many physicians in the US have followed that pathway. To learn more about it, start here: http://www.usmle.org/