Can I manually enter the correct amount of stimulus money I'm eligible for since turbotax has the incorrect amount?

You are not supposed to enter the amount of stimulus you think you are "supposed"  to get.   You are supposed to enter what you DID receive and let the software calculate whether you should be getting more.   If you are supposed to get more it will show up on line 30 of your Form 1040 and add to the refund that shows on line 34.

For the first two stimulus checks you could receive stimulus money for a dependent child who was under the age of 17 at the end of 2020.   If the dependent was older than 16 at the end of 2020 you do not get the recovery rebate credit for them.

If you enter your dependents correctly and enter the amount of stimulus that you actually received for each of the first two checks, if you are getting more it will be calculated.

The third stimulus is a separate check and there is no place to enter anything about it on your 2020 return.