No, they are entirely separate infections. You can't get chlamydia unless you have sex with someone with chlamydia. And chlamydia isn't transmitted by oral sex.
Best wishes-- HHH, MD
These are two completely different diseases. Cold sores are usually caused by the HSV-1 virus and can be transmitted through oral sex. Chlamydia is another disease that is spread usually through unprotected vaginal intercourse with some who is infected. In very rare instances it can be spread by oral sex. I hope that this helps. There are numerous posts on the site dealing with both of these diseases.