Yes it is possible for sexually transmitted infections (STI) to pass when having oral sex, but you or your gf would need to have an STI for there to be any chance of this happening.
Have a look at our “Know your chances” web page, it provides information on your chances of getting or passing an STI depending on how you are having sex.
It is also common that many STI do not show symptoms, given this we recommend that people go for STI testing. How often you get STI testing really depends on your personal situation. Have a look at our page on when to test.
Have a look at our “STIs at a glance” chart, it provides information on how long you need to wait before getting tested (window period).
Please leave a comment to let us know if this answers your question or if you need more information.
For other readers, please feel free to leave a comment, or let us know if this was helpful.