I am not licensed in your state but I can offer some general advice.
This question would be better posted in the Estate Planning section but I will try to help.
No, but you still will be. Once you die your estate will still be liable to repay your debts. So if you die with a bank account with $10,000 in it before your son gets any of that money your creditors will.
Of course the order in which people get paid from your estate differ from state to state. But typically your estate will pay your burial expenses, then legal expenses, then states, then your creditors, then to your heirs.
You can avoid at least some of that by taking your estate out of the probate process, for example if your bank account was joint with your son he would just get the account when you die.
You should talk to an estate planner to best plan for your passing.
You should talk to a local lawyer who will be able to help you with your case.
Your son would not be responsbile for the debt unless he cosigned on the debt. When someone passes away in Ohio creditors may file a claim against probate assets. Probate assets are any assets that are only in your name and do not have a beneficairy designation.
Be careful about making someone a joint owner of your asset this can have some very bad unintended results.
I would encourage you to talk to an estate planning attorney.