I need to download my returns from 2015 from my account which has Turbo Tax Deluxe, but it says I have to upgrade to download.

Have you paid?  

To pay the TurboTax online account fees by credit card so you can access your prior year online tax returns, click on Tax Tools on the left side of the online program screen.  Then click on Print Center.  Then click on Print, save or preview this year's return.  On the next page, to pay by credit card, click Pay Now.  On the next screen just click on the Continue button.  The next screen will show a review of your Fees, click on Continue.  Complete the next screen to pay by credit card and click Continue.

If you have found the 2015 PDF, but it's asking you to upgrade and pay to access, the method to do that depends on what all you have done for your 2018 return.   We can tell you all the steps.

Have you filed a 2018 return in Online TurboTax, or is one in preparation?  Or did you file elsewhere?

Was the 2018 return prepared in Free Edition or a paid edition?

Is the 2018 return in the SAME account as the 2015 online return?

We can tell you how to unlock a return once you answer all the questions above.   For people who used Free Edition for 2018, the upgrade would be to PLUS for 19.99.   You, however, appear to be using Deluxe.   Is that the product you needed for your 2018 return, or did you already try to upgrade and upgraded too far?   Deluxe is 59.99 for a Federal return and 44.99 for a state return.    If you haven't filed 2018 and don't need Deluxe, we can tell you how to downgrade to Free Edition, then upgrade to PLUS.

If you have already filed the 2018 return and upgraded too far after filing, you won't be able to downgrade it yourself.   We can tell you how to phone Customer Support to ask them to unlock the 2015 PDF.

There's also a free option if a return transcript will suit your purpose.  You may be able to immediately download one at the IRS website if you qualify to open an IRS account there.  Otherwise, to order a transcript to come by postal mail takes 5-10 calendar days.
http://www.irs.gov/Individuals/Get-Transcript