If you are a U.S. citizen, you may receive your Social Security payments outside the United States just like you were inside the United States. You are eligible for them the same as if you were in the United States all year.
Complete information for citizens and non-citizens is in the publication at http://www.socialsecurity.gov/pubs/10137.html#what
Likewise, a citizen does not lose any Medicare eligibility due to being outside the United States for part of the year.
Of course, there is very limited coverage outside the United States that Medicare will pay for servces outside the United States. For more details see the publication at http://www.medicare.gov/publications/pubs/pdf/11037.pdf
I hope this helps to know you can still be covered since you are a citizen.