No, you can't carry over donations.
For 2020, there is a special $300 deduction for money-only donations (cash, check, charge) that you can take if you take the standard deduction. This is not entered in the normal place for donations, but later in the program, and is shown on form 1040 line 10b. If you itemize your deductions, the value of any donations is listed on schedule A, along with your other itemized deductions, and you can deduct the value of items as well as direct money contributions.
Turbotax would not have let you claim but itemized deductions on schedule A and the special charity deduction on line 10b. If you took the standard deduction, the actual tax impact of listing your individual donations might not actually benefit you. If you itemized your deductions on schedule A but only listed $300 of charity donations, that was your misunderstanding--the program would not have limited you in that way--and you would have to amend to add any new donations.
It sounds like based upon your entries when you prepared your original return, your standard deduction was higher than your itemized deductions. This would have allowed you to claim the $300 above the line adjustment.
You will not be able to carry forward your charitable contributions. They would only be deductible in the year of the donation.
I recommend looking at your total itemized deductions and comparing it the standard deduction amount that applied to you for your filing status in 2020.
If you determine the total amount of your charitable contributions would allow you to itemize, you should amend your return to include those donations.
If adding the donations does not allow you to itemize, there would be no overall effect on your tax return and you would not need to amend as your tax return will not change.
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