Minecraft downloaded where to register?

I just bought and downloaded Minecraft Java for my PC, I just got an email from the Mojang team on my cell phone, confirming the purchase.

Now I have tried to log into Minecraft (I only had the trial version before), but as soon as I try to do so, it tells me that I should buy the full version first.

But what I've already done! Now I don't know how to open the full version or how to register somewhere.

Have you also installed the full version? It could be another launcher. Simply register on the site and download again.

I think I was on the official Mojang site and installed Minecraft, I'll log in there again and try it.