Booked flight with wrong email, will check in work?

Hello, I booked a flight last night.

However, I noticed too late that I had entered my email address incorrectly.

The ending should be .de and I accidentally made it .com.

Well, I called the airline, they confirmed the booking and sent me a confirmation via SMS with a link.

My question now: the lady said I can just go to check in, give my details and show my ID and then I'll get the plane ticket.

Does anyone know anything about this? Is this true?

I'm so panicked right now that it won't work.

Thank you very much for any help