Show Different Header on a Specific Post ID

In your header.php file, you can test which page is loading and modify the markup based on this condition. For your example, the is_page() function seems ideal.

<div style ="float: right; margin-top: 10px;">
    <p class="headersample3">
    <?php if ( is_page( '###' ) ) { ?>
        <a href="https://wordpress.stackexchange.com/questions/359723/tel:555-555-5555">555-555-5555</a>
    <?php } else { ?>
        <a href="tel:888-888-8888">888-888-8888</a>
    <?php } ?>
    </p>
</div>

Replacing the ### with your actual page ID.

If you truly need to load an entirely different header file for this one page, then you would test is_page() in the page template and then conditionally load the header file you want.

if ( is_page( '543' ) {
    get_header( '543' );  // file name is actually header-543.php
} else {
    get_header();
}

Note: The parameter passed to get_header() is not the full file name. See the Codex for more detail https://developer.wordpress.org/reference/functions/get_header/

Also, a good naming practice is to follow the WP core standards. A header for a specific page ID should be named header-pageid.php

EDIT: updated to reflect code added to question.