I didn't get a 1099. Do I owe tax?

Yes - All money or items of value (barter or trade) you receive for selling merchandise and providing services is taxable whether or not you receive a 1099.

It's your customer's responsibility to file 1099s. If they don't, that's their problem. You still must report the income. And there's no minimal amount.

I got a 1099 instead of a W-2.

If you got a 1099 but think you were actually an employee and should have received a W-2, you can challenge that by filing IRS Form SS-8, Determination of Worker Status for Purposes of Federal Employment Taxes and Income Tax Withholding. If you don't want to wait for the IRS to respond before filing your income tax return, you can enter the 1099 amount as wages and attach Form 8919, Uncollected Social Security and Medicare Tax on Wages. Note that the SS-8 must be filed separately from your 1040. Important: Be sure to carefully read the instructions for both forms.