People have given you some good ideas, but here's another: DuckDuckGo has free email aliases. You generate a "duck" address and it's just some random email address that gets forwarded to your real email address while also blocking any trackers in the emails. And you can easily turn off an alias if it becomes spammy.

It's free and you don't even have to make an account of any kind. To "log in" to their web browser and use this feature, all they do is send you an email with a link to click to make sure own that target email address. Then you can generate unlimited aliases that get redirected to it. But it's up to you to track which alias was given to which website.

There's also a master duck address that you make up manually. I guess that's technically an account and that's the one you "log in" with if you install the browser on another device. You don't have to actually use their browser, and they even have a plugin for Firefox to generate the aliases.

Not as easy as having your own domain and forwarding email going to any address to your real account, though. But it's totally free.