Usually not. By "strep throat symptoms, " I think you mean sore throat, fever, swollen glands, and tiredness lasting more than two or three days. These are not unique to strep, and usually don't occur with std's. But if you have those symptoms, you should visit your doctor to be checked.
Yes, gonorrhea. Certain STDs can cause sore throat, especially gonorrhea. You should go to a health center with expertise in testing for and treating STDs for appropriate testing.