If a provider just sends a vaginal specimen for culture, most labs will not test it for chlamydia. A chlamydia test usually must be requested. If you are at risk for STDs, you should ask your provider to test for both chlamydia and gonorrhea. (The provider might be planning to do that anyway, but it is wise to be safe and make sure.)
You are right to be concerned. Instrumentation of the uterus in the presence of a cervical chlamydial infection (or gonorrhea, for that matter) risks carrying the infection into the uterus. If that happens, often there are no symptoms at all. When symptoms occur, they are the same as for any uterine or tubal infection (endometritis or pelvic inflammatory disease [PID], respectively): low abdominal pain and fever are the main symptoms. The ovaries do not become enlarged, but serious cases can be associated with tubo-ovarian abscess, a serious complication.
Chlamydial infection prior to conception can interfere with conception. In fact, some women who have trouble conceiving and are suspected to have chlamydia are able to become pregnant after treatment for chlamydial infection. And in general any infection in the uterus is potentially harmful to an early pregnancy--although I am not aware chlamydia has been shown to be a problem at that stage. If a woman still has chlamydia late in pregnancy (or if she acquires it during pregnancy), the baby can get infection of the eyes or pneumonia.
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