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.
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