Can I just file for my business instead?
Yes, you can but it may not do much good. You may need to consider personal bankruptcy.
A non-living legal entity like a corporation or an LLC can file bankruptcy. But unless you plan to reorganize it under a Chapter 11, it won't discharge any debt. So it won't typically do you -- or your business -- any good.
If your business is a sole proprietorship -- that is, it has no separate legal entity -- or a partnership, even if you obtained a fictitious name to use, then there is no separate business. You are the business.
Keep in mind that for most substantial debt your business owes, it is also owed often by you personally as well. There were probably personal guarantees you signed promising to repay the debt if your business did not. Bankruptcy only helps wipe out this guarantee if you file personally.
On the positve side, a person who has a majority of his debt from business (non-consumer) sources cannot be forced into a repayment plan instead of Chapter 7. So even if you have substantial income after the failure of prior business, you may be able to move on rapidly.
Further reading: Just File for My Business, Please!