I gave oral sex to my girlfriend now i've suddenly come with a bacterial infection on my tonsils, should i ask my girlfriend to get checked?

Yes, check both/both: That means both people can be checked in both places, upstairs and downstairs. That means checking the throats for strep throat infection, and checking the penis and vagina for chlamydia and gonorrhea... which is fortunately easy to do by the modern tests that use a urine sample (instead of a swab into the penis or into the vagina). If "high risk" for STD's, other tests can be considered.