So I am adding a webpage to an already existing website that would take information hopefully through a form and have a pin on a map that points them to it. Should I use wordpress or making a PHP(a language that I know) file.
If you have no expierence with web development, it's maybe a good idea to start with a (auto updating) CMS/Framework like wordpress because of security reasons. The GUI helps you to get fast results.
If you want to dig into web development or if you are expierenced, it would produce less overhead to program your (simple) tasks directly with PHP or another language.
You can definitely use PHP as the P part of a LAMP stack.
However, for the sake of your personal sanity I recommend using a framework like laravel which does some of the backend work for you. It definitely adds a bunch of security without forcing you to learn how to do secure prepare SQL queries.
There are dozens of frameworks to choose from.
Just make sure you choose one that is still actively being developed. That way when issues are found the developer will fix them.
Should I use wordpress or making a PHP(a language that I know) file.
Given that you would probably have to convert the entire existing site to WordPress (even if not, you would have to learn WP and add some dependencies to your site), this seems like a no-brainer. Code some PHP. What would you gain from Press.
For the map, I highly recommend Leaflet wrapped around Open Street Maps. Your PHP would generate an HTML page with some very simple JS to show the map.
S.O question Using Leaflet map in php page