Not to scare you, but Hep B is actually known to be 100 times easier to catch than HIV. It is an extremely infectious STD. Then again, I've had my former partners tested since finding out I have Chronic Hep B and not a single one one of them was exposed. And by the way, exposure during sex does not not only mean intercourse but oral sex too. Hep B is transmitted just like HIV is: mother to child during birth, blood and other bodily fluids, needles etc. The good news about Hep B is that 90% of adults who get it clear it out of their system no problem. Many people don't even know they have it. Incubation period is anywhere from 1-4 months.
Hep C, on the other hand is not considered an STD. It is transmitted only via blood to blood contact. The chances of it being transmitted through sex alone is extremely low. But as both CaryF and Dansbrother suggested, that does not mean you should not practice safe sex.
If you are concerned that you may be have been exposed to Hep B or C, you should ask your sexual partner. Either way, it's essential to practice safe sex and to be tested at least once a year for STDs. Good luck to you and I hope everything works out.