Rate limits are applied to users or applications, so the server themselves would not affect that. Some developers run into into issues when they move from a single dev server environment to a multi server prod environment. Make sure your application does not have any type of behavior that is being executed by all of your servers. For example, a polling background task on one server might be fine, but if that background task somehow now runs on all of your servers in the prod environment you may hit rate limits.
I would also suggest configuring the environment that was working to use the new Twitter account. If you have the same issue then it is the specific Twitter account and can use this form to inquiry why that account is being rate limited differently. If it works then it’s not the account and you know its something to do with your server environment and app architecture.