Why did my payment go up when I entered my 1099-R? I already had taxes taken out when it was distributed.

The taxable amount of the withdrawal is added to your other taxable income thereby increasing your tax liability.  The federal taxes withheld are added to the other federal taxes withheld, if any, reported on your tax return.

The tax that was withheld when you took money out of the retirement account was an estimated amount--just like when an employer withholds money from a paycheck.   When you enter all of your income and all of the tax that was withheld into the software, the software does the calculations and reconciles the tax you had withheld with the amount that you need to pay.