I got a few minutes and made the custom code for you.
Copy and paste this in your themes functions.php
remove_shortcode('gallery', 'gallery_shortcode');
add_shortcode('gallery', 'gallery_shortcode_custom');
function gallery_shortcode_custom( $attr ) {
$post = get_post();
static $instance = 0;
$instance++;
if ( ! empty( $attr['ids'] ) ) {
// 'ids' is explicitly ordered, unless you specify otherwise.
if ( empty( $attr['orderby'] ) ) {
$attr['orderby'] = 'post__in';
}
$attr['include'] = $attr['ids'];
}
/**
* Filter the default gallery shortcode output.
*
* If the filtered output isn't empty, it will be used instead of generating
* the default gallery template.
*
* @since 2.5.0
* @since 4.2.0 The `$instance` parameter was added.
*
* @see gallery_shortcode()
*
* @param string $output The gallery output. Default empty.
* @param array $attr Attributes of the gallery shortcode.
* @param int $instance Unique numeric ID of this gallery shortcode instance.
*/
$output = apply_filters( 'post_gallery', '', $attr, $instance );
if ( $output != '' ) {
return $output;
}
$html5 = current_theme_supports( 'html5', 'gallery' );
$atts = shortcode_atts( array(
'order' => 'ASC',
'orderby' => 'menu_order ID',
'id' => $post ? $post->ID : 0,
'itemtag' => $html5 ? 'figure' : 'dl',
'icontag' => $html5 ? 'div' : 'dt',
'captiontag' => $html5 ? 'figcaption' : 'dd',
'columns' => 3,
'size' => 'thumbnail',
'include' => '',
'exclude' => '',
'link' => ''
), $attr, 'gallery' );
$id = intval( $atts['id'] );
if ( ! empty( $atts['include'] ) ) {
$_attachments = get_posts( array( 'include' => $atts['include'], 'post_status' => 'inherit', 'post_type' => 'attachment', 'post_mime_type' => 'image', 'order' => $atts['order'], 'orderby' => $atts['orderby'] ) );
$attachments = array();
foreach ( $_attachments as $key => $val ) {
$attachments[$val->ID] = $_attachments[$key];
}
} elseif ( ! empty( $atts['exclude'] ) ) {
$attachments = get_children( array( 'post_parent' => $id, 'exclude' => $atts['exclude'], 'post_status' => 'inherit', 'post_type' => 'attachment', 'post_mime_type' => 'image', 'order' => $atts['order'], 'orderby' => $atts['orderby'] ) );
} else {
$attachments = get_children( array( 'post_parent' => $id, 'post_status' => 'inherit', 'post_type' => 'attachment', 'post_mime_type' => 'image', 'order' => $atts['order'], 'orderby' => $atts['orderby'] ) );
}
if ( empty( $attachments ) ) {
return '';
}
if ( is_feed() ) {
$output = "\n";
foreach ( $attachments as $att_id => $attachment ) {
$output .= wp_get_attachment_link( $att_id, $atts['size'], true ) . "\n";
}
return $output;
}
$itemtag = tag_escape( $atts['itemtag'] );
$captiontag = tag_escape( $atts['captiontag'] );
$icontag = tag_escape( $atts['icontag'] );
$valid_tags = wp_kses_allowed_html( 'post' );
if ( ! isset( $valid_tags[ $itemtag ] ) ) {
$itemtag = 'dl';
}
if ( ! isset( $valid_tags[ $captiontag ] ) ) {
$captiontag = 'dd';
}
if ( ! isset( $valid_tags[ $icontag ] ) ) {
$icontag = 'dt';
}
$columns = intval( $atts['columns'] );
$itemwidth = $columns > 0 ? floor(100/$columns) : 100;
$float = is_rtl() ? 'right' : 'left';
$selector = "gallery-{$instance}";
$gallery_style="";
/**
* Filter whether to print default gallery styles.
*
* @since 3.1.0
*
* @param bool $print Whether to print default gallery styles.
* Defaults to false if the theme supports HTML5 galleries.
* Otherwise, defaults to true.
*/
if ( apply_filters( 'use_default_gallery_style', ! $html5 ) ) {
$gallery_style = "
<style type="text/css">
#{$selector} {
margin: auto;
}
#{$selector} .gallery-item {
float: {$float};
margin-top: 10px;
text-align: center;
width: {$itemwidth}%;
}
#{$selector} img {
border: 2px solid #cfcfcf;
}
#{$selector} .gallery-caption {
margin-left: 0;
}
/* see gallery_shortcode() in wp-includes/media.php */
</style>\n\t\t";
}
$size_class = sanitize_html_class( $atts['size'] );
$gallery_div = "<div id='$selector' class="gallery galleryid-{$id} gallery-columns-{$columns} gallery-size-{$size_class}">";
/**
* Filter the default gallery shortcode CSS styles.
*
* @since 2.5.0
*
* @param string $gallery_style Default CSS styles and opening HTML div container
* for the gallery shortcode output.
*/
$output = apply_filters( 'gallery_style', $gallery_style . $gallery_div );
$i = 0;
foreach ( $attachments as $id => $attachment ) {
$attr = ( trim( $attachment->post_excerpt ) ) ? array( 'aria-describedby' => "$selector-$id" ) : '';
if ( ! empty( $atts['link'] ) && 'file' === $atts['link'] ) {
$image_output = wp_get_attachment_link( $id, $atts['size'], false, false, false, $attr );
} elseif ( ! empty( $atts['link'] ) && 'none' === $atts['link'] ) {
$image_output = wp_get_attachment_image( $id, $atts['size'], false, $attr );
} else {
$image_output = wp_get_attachment_link( $id, $atts['size'], true, false, false, $attr );
}
$image_meta = wp_get_attachment_metadata( $id );
$orientation = '';
if ( isset( $image_meta['height'], $image_meta['width'] ) ) {
$orientation = ( $image_meta['height'] > $image_meta['width'] ) ? 'portrait' : 'landscape';
}
$output .= "<{$itemtag} class="gallery-item">";
$output .= "<p>$attachment->post_title</p>";
$output .= "
<{$icontag} class="gallery-icon {$orientation}">
$image_output
</{$icontag}>";
if ( $captiontag && trim($attachment->post_excerpt) ) {
$output .= "
<p>
" . wptexturize($attachment->post_excerpt) . "
</p>";
}
$output .= "</{$itemtag}>";
if ( ! $html5 && $columns > 0 && ++$i % $columns == 0 ) {
$output .= '<br style="clear: both" />';
}
}
if ( ! $html5 && $columns > 0 && $i % $columns !== 0 ) {
$output .= "
<br style="clear: both" />";
}
$output .= "
</div>\n";
return $output;
}
If you need to add a custom class to your p tag modify
$output .= "<p>$attachment->post_title</p>";
and
<p>
" . wptexturize($attachment->post_excerpt) . "
</p>";