im manually inputting the information for my t2202, am i able to use my t2202 from 2020 and 2021 for my 2024 taxes?

You would have to enter your T2202 for 2020 into your 2020 return. The same thing goes for the T2202 for 2021. Any amounts tuition amounts that are left over from 2021, 2022 & 2023 will carry forward to 2024.