Do I need appium to run selenium script to run in Mobile Browser?

Hi I am working for one ecommerce company. We have selenium automation for web based application. We don’t have any app since we have our website only. Now my manager is asking me to start with appium to run all my selenium script on Mobile browser so the way we can use our real device to test. I was wondering do i even need appium to run our Selenium automation script on Mobile Browser ? Please help me with appropriate answer. Thanks