It can be common for woman to have spotting or bleeding between periods with chlamydia, but there are other conditions that are non-STI that can cause this as well e.g. changes in hormone levels, stress etc…
I would recommend going to see a health care provider, they would be able to talk to you about your medical history and do some testing to see what could be causing the problem.
It doesn’t sound like PID (Pelvic inflammatory disease) as the most common symptom with PID is pain in the lower abdomen, but I have seen some woman in the past that only had the lower abdomen pain when the cervix was moved during the PID check. Given this it would be good for the healthcare provider to do a PID check just to make sure. Here is a link for more information about PID.
It doesn’t sound like chlamydia would be causing the bleeding as you were treated for this and your follow up test was negative. It also sounds like you have not had sex since the follow up test; let me know if I got this wrong.
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