If your long-term plan is to stay in the US, your best bet is to invest the 3 years into an internal medicine residency. Down the line, this saves you a lot of trouble getting permission to practice at individual hospitals (you want to do at least 2 years of regular residency in order to be licenseable in all states).
Given your prior foreign triaining, you might be able to get the american board of internal medicine to allow you to do 1 year of your training in the form of a fellowship. Being a fellow is intelectually more rewarding than a third year resident.
Immigration wise, you should talk to an attorney familiar with 'outstanding researcher' 'extraordinary ability' and 'national interest waiver' type immigration petitions. You might be able to get your green-card before you even come to the US. This would open worlds of trainintg opportunities not available to the average applicant who needs a J1 or H1b visa for their residency.