It is possible to pass on STDs and STIs by oral sex as the lining of the mouth is very thin and so small tears and transmissions are quite common.
Specifically for those giving oral sex Better2Know would recommend a Chlamydia and gonorrhoea test of your mouth. This test would take a small swab from your mouth, and your results would be ready in two days.
If you are worried that you had a cut in your mouth then there is a low possibility of HIV transmission and you should consider including an HIV test.
Everyone’s circumstances are different, and it is your responsibility to choose the tests that are right for you depending on your sexual activity and what you know about your partner. If you are unsure then Better2Know recommends a Full STD screen. Once is enough to catch an STD, STI or HIV.