Sorry for the issue you're encountering.
For reference, our official embedded widgets don't require you to create API keys, but it sounds like you're using an alternative solution.
We request that developers have a verified phone number associated with their account so as to reduce the cases where spammers and others create many accounts and many apps to abuse the API - which I understand you're not doing here, but I'm just explaining the context.
If you're unable to add a phone number to your account for some reason, you should raise a ticket with us. Please use the last form option on https://support.twitter.com/forms/platform and a member of our platform operations team will assist you when they are able to process the ticket.