It seems you have an acute HBV infection. Please test again your HBV serology after 3 months (6 months from appearance of symptoms). Hopefully, you would have recovered(as most adults do) from the acute HBV infection and not become chronic. All the best.
The answer is yes and no. You have resolved your HBV infection and is no longer considered as infected with Hepatitis B. You will find your HBcAb will test positive. You are like the estimated over two billion people who were exposed to HBV and resolved the infection. But recent discovery indicated that your liver still has some cccDNA that will still produce some HBV virus, however, the virus is controlled by your immune system, resulting in HbsAg negative and hbvdna undetectable. Should you in the future require medical treatments that weaken your immune system, such as cancer chemotherapy, anti-inflammation treatment for arthritis, then there is a chance that your HBV will re-activate. Nowadays, doctors are very well aware of this possible re-activation in HBcAb positive patients and will prescribe HBV antiviral treatment beforehand.