Can I file 1099-NEC income along with 1099-R, DIV and INT? It looks like my 199 NEC was added to my total income, taxes were figured, and then self-employment tax added.

Yes that's how it works.  

You pay Self Employment tax (Scheduled SE) on a Net Profit of $400 or more on Schedule C.  You pay 15.3% SE tax on 92.35% of your Net Profit (If it is greater than $400).  The 15.3% self employed SE Tax is to pay both the employer part and employee part of Social Security and Medicare.  So you get social security credit for it when you retire.  

The SE tax will be included in your tax due or reduce your refund.  It is on the 1040 Schedule 2 line 4 which goes to 1040 line 23.  The SE tax is in addition to your regular income tax on the net profit.  You do get to take off the 50% ER portion of the SE tax as an adjustment on 1040 Schedule 1 line 15 which flows to 1040 line 10.

Yes, you can enter all of those forms separately.  You will need to include ALL income from ALL sources on the same return.  If you have any W-2's you would include those as well. 

Why does it seem your self-employment income was taxed twice?  Did you enter the same income in different parts of the return?  If you account for your income with your own records and that included the income on the 1099-NEC, then you would not add the 1099-NEC.

Your self-employment income is subject to an additional 15.6% self-employment taxes in addition to your regular income tax so if you seen a big jump, it would be due to the additional taxes on self-employment income. You will see your Self-Employment tax on line 23 of your 1040. 

Did you by any chance have an underpayment penalty for not making quarterly payments on your self-employment income?  If you did not pay at least 100% of your 2021 tax liability or 90% of your 2022 tax liability, you could be subject to an underpayment penalty.  If this is the case, you can walk through form 2210 by selecting Other Tax Situations>>Show more next to Additional Tax Payments>>Start next to underpayment penalties. 

If you walk through step by step in the income section, you will be able to enter all of your tax forms.  This is the best way to use TurboTax to be sure you do not miss or skip any entries.