“File menu > Save” produces “Audacity Projects” which are not normal audio files.
“File menu > Export” must be used to create an ordinary audio file.
Ensure that you don’t use dots “.” in the file name. Audacity will automatically add the “.mp3” file extension to the name that you provide, but only if the file name does not contain any dots.
Are there any error or warning messages when you export as MP3?