$5370+$3220 =$8,590, not $8550.
A 1099-SA reports withdrawals (distributions), not contributions. Is that the confusion? The 1099-SA shows what was paid to you or your providers, and it can't be changed unless it actually shows an incorrect withdrawal amount.
Someone needs to look at your form 8889 and the associated worksheets. You can't view those forms directly if you are filing with Turbotax online. That's what customer support should have helped you with. (You can view those forms directly if you are using the desktop program installed on your own computer, let us know if you are using the desktop program.)
If you are using TT Online, you may want to call support again and try and get someone more knowledgable. Or, go to the support menu and look for "send file to agent". This uploads an anonymous version of your file to tech support and gives you a token number so that someone can associate your case with that anonymous file. Post the token number here and I can try and get a moderator to look at your case.
