For the IRS, you need to file an amended return making your corrections. However, because you have received a notice, you need to respond to that notice with your amended return rather than just filing it online.
For PA, it's similar. Once you've received a notice, you respond to the notice with documentation.
Regarding continuing to use TT, you have a point. You have identified several times where you entered incorrect numbers. One way to avoid this is to have someone else enter the numbers. This means hiring a tax preparer locally or online. TT spent most of the tax season advertising their version of this service "TT Live." You can also go to a local CPA or other enrolled tax preparer of your choice.
