Can a missed period for two months mean you have a std or is that even possible. Can a std make you stop your period?

Not usually. The most common symptom with STD's is pain , irregular bleeding, and sometimes fever. The most common reason for period arrest is pregnancy, so if you are sexually active do a pregnancy test.
No . Sexually transmitted infections do not cause changes in the menstrual cycle. If you think you might be pregnant check then check a home pregnancy test. They are cheap, reliable and available at any pharmacy. Get tested for STDs if at risk. .