Your specific problem is solved, but just for people reading this thread who may be confused about some concepts:
Your instance of Lemmy or Mastodon, whichever it may be, is just one website that serves as a Reddit or Twitter clone respectively. There isn't a lot of difference between one single instance of Lemmy or Mastodon on the one hand, and Reddit or Twitter on the other. Just like you need to register and log in on Reddit or Twitter if you want to interact there, you need to do the same on any instance of Lemmy or Mastodon you want to interact on.
So what is the concept of federation then? It doesn't mean you can log into one website with the credentials of another website. All that federation means is that the website downloads some of its data (posts, comments, status updates, whatever) from other websites running the same or compatible software, instead of getting all of it from its own users (like Reddit and Twitter do).