There are usually free STD clinics at the county health departments. They check for chlamydia, gonorrhea, hepatitis, HIV, and syphilis. I wish that it was routine for them to check for the many other bacterial, fungal and viral infections that can be associated with and communicated via sex. (Herpes, for example)
However, at least these things are checked for.
Yes, the bacteria that potentially live in your (a man's) genital tract can/do multiply and live in the female genital tract. The bacteria that are in the intestines can cause harmful infections in other parts of the body, thus we are trained to wash our hands after defacating. The genital tract is an opening into the body just as the mouth, any abrasion to the skin, and your eyes.
You always should wear a condom, always.
Anal sex is usually painful if not done right. First of all, the woman has to be very turned on for it to be pleasurable to her. Second of all, it takes time for the muscles around the anus to relax and allow for penetration. The head of the penis has to be inserted carefully, then wait for her muscles to relax. Then proceed.
TELL your girlfriend asap! She will probably be wise to be checked for all the things you are as well as be treated for whatever the doc recommends you be treated for.
Good luck.