Should I put my $3300 AirBnb earnings in the business income or personal income category?

It depends on the nature of your rental; please read below:

If you rented the rooms for 14 days or less, you are not required to report the rental income. But you cannot deduct any related expenses, either.

Occasional, short -term rental with no guests services may be deducted as personal income, in the rental section:

1. Federal Taxes
2. Wages & Income
3. Rental Properties and Royalties - follow the instructions  Where do I enter income and expenses from a rental property?

If you dedicate a room in your home solely for the paying customers, never live in that room and provide services such as regular cleaning or maid service, provide coffee or breakfast,  you may be considered "running a business".  In this case, you would deduct  your income and expenses as self-employed income, subject to Social Security and Medicare tax.

1. Federal Taxes
2. Wages & Income
3. Business Items
4. Business Income and Expenses (Sch  C)- you may be asked to upgrade to Self-Employed version.