It all depends
If she was clean before she serviced the guy with Chlamydia the chances are not too great that there would still be enough organisms in her mouth to be transferred to you to cause an infection, but there is still some possibility that you could be infected.
Cuts in the mouth are of no significance with Chlamydia as it is a disease of the mucous membranes, and is not found in the blood stream as is HIV, syphilis, Hepatitis etc.. Chlamydia infects the urinary tract in men (even as far back as the prostrate) as well as the mouth, oesophagus and lungs if contact was oral. In women it is principally a vaginal infection that can travel through the uterus to the fallopian tubes etc., causing severe problems if left untreated, as well as an oral infection as mentioned above.
Chlamydia, should you be so unlucky as to get it, is very easily cured with a single dose of oral medication.
Worry more about Herpes, HIV etc. which are uncurable!