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.
