It is possible to get an STD from oral sex. Apparently there was recently something of an epidemic of gonorrhea in high-school aged kids because they didn't think they could get anything from oral sex, and they used it as a substitute for any other kind of sex This does not mean any time you have oral sex, you will get an STD, but it is worth taking precautions since there is the risk.
HPV shots prevent HPV only. They do nothing to guard against gonorrhea, chlamydia, syphilis, HIV, herpes, etc.
If you are worried, it's possible to get tested for all the sexually transmitted diseases and conditions. If you are not so worried because of the lack of symptoms, use condoms. Keep an eye for slow-developing conditions as well.
Planned Parenthood is a good source of information, sometimes they even have classes to attend about all this stuff. I don't think you should be having sex until you are completely ready either, it's not supposed to be an experiment where you wind up scared, but a loving act done with someone you really care about and are turned on to be with.