Why do you need to create apps for those sites? if you are embedding Twitter timelines or Tweets, you can do so without the need to create an app using the tools at publish.twitter.com
If you must create apps, then yes, you’ll need a verified phone number attached to a Twitter account before you can do so. This is a safety measure we take to avoid the abuse of the API. You could create multiple apps against a single account and use them for different sites not directly associated with that account, but note that you are limited to the number of apps you are allowed to create per account and originating IP address per day.