I have added new page layout and component in the managed package and created a new version, but when I'm doing push upgrades, the changes are not getting into the org. Is there any way to automatically deployed this page layout?
No, page layouts don't automatically upgrade. You could attempt a metadata deploy in a post-install handler, but since the Metadata Toolkit is asynchronous, any errors won't be reported back, and you won't have another chance to do so until the next upgrade. For now, you must be prepared to either update all your clients' layouts, or provide instructions on how to do so. A structured release cycle will help minimize the number of times your clients will have to update their page layouts.