Is there an email service that lets you choose what is between the @ and .com without having to pay $?

I know that normally you can do that if you buy a domain name but im in a but of a pickle. I have an account that a friend made for me many years ago and she used a fake email just putting myname@randomletters.com, problem is now after getting hacked i changed the password but i believe mis-spelled it and am locked out. I cant have it email me the password because the email doesnt actually exist. Which is where actually makintg that email account comes into play. But not sure how to phrase in a search and look it up. :(

What do people think?

• To help choose the perfect domain name, get help from us at domain naming service. For £25 submit your request and a limitless number of contributors will send you domain name suggestions over a period of 30 days, all you have to do is pick the one you like. If we can't help you, we will refund you. Find out more at domain naming service
• Nope. That would be the domain name, and domains cost money. And if you bought a domain, you'd have to set up an e-mail server on it, which is even more money.