You certainly don’t need to purchase the app twice. First, make sure you have wifi connectivity. Next, make sure you are logged into the same Google Play account that you purchased the app from. Next, close your app and reopen it. µTorrent should turn into Pro automatically (it pings Google Play to verify that you have bought the upgrade). You will know it is Pro because the app's name will now be listed as uTorrent/BitTorrent Pro under the menu icon in the upper left corner of the app.
If you bought Pro as a standalone app (not from within the app as an upgrade), you can re-download Pro directly from Google Play. Make sure you are logged into the same Google Play account that you purchased the app from, and µTorrent should turn into Pro automatically.
If none of these suggestions help, or if you accidentally purchased Pro twice, please contact us and we will help you sort it out.