After entering 1099s, it says I owe $437 in self-employment tax, which would be 14.12%, yet I watched it deduct $1181 from Fed

When you enter your self-employed income on form 1099-NEC, there are several things happening to your tax refund, which can explain the $1,181 drop in refund:

1. Your self-employed income of $3,094 is subject to income tax which is at your marginal tax bracket whih depends on your total taxable income
2. Your self-employed income is subject to self-employment taxes of $347. This is correct for $3,094 of SE income.
3. Certain credits such as the Earned Income credit may be decreased as your income increase. The Earned Income Tax credit (EITC) is a bell shaped curve against income. The EITC rises with income until a certain level of income when it starts to decrease to reach 0 at the maximum level of income for the category.

As an example, please look at the EITC tables from page 33 of this IRS publication.