It's easier to switch the other way--i.e., from the online version to your desktop product. I'll mention that option lower down in this post. But first I'll address what you actually asked.
If you want to try to work something out about continuing to use the Online version, I can tell you how to reach TurboTax Support below. The pricing structure and features are much different between the 2 products. For instance, the desktop Premier includes state return preparation already, while in the Online version a state return is an extra 36.99 (39.99 later in filing season.) So it's not an even trade, and I don't know what they will tell you on how to handle it.
The desktop version also has Forms Mode for direct viewing/editing of forms, and can prepare multiple returns. It can also prepare a Schedule F and Schedule C with expenses that the Online Premier cannot handle.
If you're just wanting to avoid paying twice, it's easy to do the other way around. You can download the *.tax2016 data file from your online return if you want to continue it in the desktop version without starting over. If you want to do that, here's how:
https://ttlc.intuit.com/questions/1901476-how-do-i-switch-from-turbotax-online-to-the-turbotax-softw...
NOTE: The state return is included in the desktop Premier program, but there is a 19.99 state efile fee (24.99 later in filing season). There is no state efile fee for New York state, and there is no fee to print and mail the state returns.
Otherwise, if you want to keep using the Online version, here's how to reach TurboTax Support to discuss your situation. When you follow the steps in the FAQ below, it will provide you a short form to fill out. Then you will be provided an incident number and a phone number. The number will not display when they are closed. Business hours are listed in the FAQ.
FAQ: How do I contact TurboTax?
https://ttlc.intuit.com/replies/5566005
