Can you get some education tax credit as a full-time student to offset 1099-NEC large self-employment tax from internship?

Yes, you can review What self-employed expenses can I deduct? for additional "ordinary and necessary" business expenses you can use to reduce your internship income.  The credit reduction you are experiencing is due to your income level reported that is reducing the credit available.

Once you have determined the expenses you can deduction you can follow these steps to enter them in TurboTax Online:

1. Within your tax return use the magnifying glass icon to search for Schedule C
2. Click the Jump to link
3. Click Edit for the line of work
4. Scroll down to Expenses and click Start or Edit if the category you want is shown
   • If you don't see the category you want listed click Add expenses for this work
   • Scroll to and mark the box for the category of expense you want to add - if you don't see it on the list, scroll down to the Less Common section and click the down arrow and show more until you do
   • Click Continue
5. Enter your expenses either as totals for each category or you can list out the different items (ie. email, website, etc.)