Check if current page is the Blog Page

If by ‘blog page‘ you meant a static page set as posts page in the Reading Settings, then you could check it by doing this:

if ( is_front_page() && is_home() ) {
  // Default homepage
} elseif ( is_front_page() ) {
  // static homepage
} elseif ( is_home() ) {
  // blog page
} else {
  //everyting else
}

When you use is_home() and is_front_page(), you have to use them in
the right order to avoid bugs and to test every user configuration.

(Source: Conditional Tags – The Blog Page)

Or simply:

if ( !is_front_page() && is_home() ) {
  // blog page
}

Or more simply (I suppose):

if ( is_home() ) {
  // blog page
}