Will making the website public cause some problems as well?
Define what problems mean to you. It's not easy to set up because first you have to reconfigure your router and the way to do that is different from router to router and then you also have to get a subscription from one of the dynamic DNS providers to make the (changing) IP address of your router available on the Internet by a fixed name. Once you have the subscription you also have to configure that account into your router (given that it supports that feature). From what I've read in this thread I'd guess that you're not experienced with networks, so this probably is a bigger problem for you.
the reason i am asking is i want to be able to access the website over my mobile data network.
Please describe what you want to achieve, what kind of data the webserver on your Arduino provides and why you think you must be able to access it by the mobile data network. Maybe we find an easier alternative for you.