You would need to have a throat swab done to check for chlamydia in the throat. A vaginal swab would not pick up chlamydia if it was in the throat.
Gonorrhea and chlamydia are the same in that you need to test each area that it could have been passed too, for example, urine test, urethra swab, vaginal swab, throat swab and rectal swab.
I don’t know your full sexual history but since chlamydia is very common, usually does not show any symptoms and can hang around for a bit of time. It may be an idea to get vaginal and anal swabs as well if you have had vaginal or anal sex before. You can always ask the health professional you see if your wondering what types of test would be good to get.
Let us know if you have any other questions or concerns.