Hello Matt,
Thank you for your medical query at DoctorSpring.com
I understand your concern.
Yes, there is a possibility of acquiring Chlamydia from unprotected intercourse. Your girlfriend has been bleeding after intercourse. Now, if you indeed passed on the infection to her, this won't be her only symptom. Invariably she will show other symptoms of infection such as burning urination, constant urge to pee, and peeing frequently along with a white discharge from the urethra. Bleeding from the vagina after intercourse is never the only symptom that a woman with Chlamydia will show, so I don't think your girlfriend has chlamydia. She needs to be physically examined by a gynecologist who can guide her further.
Hope this was helpful,
Regards.