Is my DBA assets protected legally from my personal obligations?

No.  DBA just means "doing business as", it is not a separate legal entity.  Moreover, even if it was a separate legal entity, like a corporation or an llc, your stock or other equity interest in that entity would be a personal asset, which can be sold to satisfy a judgment against you.  For example, if someone has a judgment against you for $10,000, he/she may be able to sell your stock in your business in order to pay off the judgment.  On the other hand, if your business is a separate legal entity, you are not personally obligated on its debts.  For example, if your business corporation can't pay its lease, the landlord can't force you to sell your house, which you own individually, to pay that obligation (providing you have operated the corporation propertly and haven't personally guaranteed the lease, but that's another story.)