In general there should be no need to apply for developer access if you just want to have a Twitter embedded timeline - you can use publish.twitter.com.
If you are looking to use a custom solution, you may need to apply for developer access. Our team works through requests for access as quickly as they can, based on your use case description. I’d suggest checking your junk/spam folder for any pushbacks for clarification in the meantime.
If you’ve changed your email address, you may need to raise a ticket via https://help.twitter.com/forms/platform