HiI'm new to QB and trying to add existing invoices that are already paid, but when I add them the invoice totals get added to my bank balance.

Presumably you are moving to QB from some other accounting system or service.

When starting a new set of books its important to have a firm cut-off date, and finalized balances in the 'old' system - so you know where to start in the 'new' system.

Generally a paid invoice will be part of the 'old' accounts - no entry in the new books or the revenue will be double counted.

If you want the'new' accounts to include income&expenses from the 'old' system that will be more complex. One fairly 'safe' way to handle that would be to create a full P&L statement in the 'old' system for just the portion of the current fiscal year up to the 'cut-off date' you set for system changeover.  Then create a single long JE exactly copying the amounts & accounts from that statement.  The Net Income line would be posted to RE. 

If you hope to bring over even more details from the old system then your basicaly going to be re-entering ALL the prior entries.