Transparent, welcome to the forum. I have hep C, though I also contracted hep B around the same time (1968 or '69.) My immune system threw off the hep B, but not the hep C. However, since I have the hep B antibodies, I will always test positive for it.
It is my understanding that hep B is highly treatable. If your liver enzymes continue to be high, perhaps it would be best to go ahead and take the antivirals that your doctor recommends.
I know we have one member whose son has chronic hep B, though she hasn't posted in awhile. Perhaps she will see this and offer some insight.
Meanwhile, please try not to worry. I'm assuming that you are not drinking or using illicit drugs, both of which are terrible for the liver. Try to eat a healthful diet with no red meat, and get enough rest. Also, learn all you can about hep B and keep us posted on how you are doing.