I would recommend you visit a friend who has internet access. Bring plenty of beverages & snacks of his/her choice to use their internet ;-}
The next choice here is to buy a USB thumb drive (or external disk) and bring it to an Apple Store so you can use their systems to download the OS installer.
The last option which I think would be more expensive (depending on your cellular service offering) is use your phone as a modem via the USB or WiFi. So you can do the install that way.
You might want to see if someone who has a Mac can prep up a bootable USB drive for you with the OS installer on it and then mail it to you. Thats what I would do in this case.
You could also give Apple a call and order the OS installer disk (Mountain Lion). Apple will charge you a fee for that.
You still need to create a bootable external drive here so you can check your internal drive. Do you have a free USB thumb drive 16GB or larger? Do you have an external drive with a backup of your stuff? If not you should get that started before doing anything.
Follow this Samsung guide to setup your phone as a hotspot: How do I Set Up and Use Mobile Hotspot or Tethering on my Samsung Galaxy S5? BIG warning here! The OS installer is a big file! As an example the current OS installer, El Capitan is 6.2GB so it will take awhile to download and your cell service may not allow you to download this large file (data cap). If it cuts out don't worry the downloader will pickup were it failed. But, you'll loose your data service for the month.
You should try to maintain your system better using your phone as a hotspot. Apple and others release updates which you should install.