How can you STOP hackers from obtaining your IP Address?

What symptoms are making you think hackers are obtaining your IP address?
 
The IP addresses you listed are both local to your network and not external.  127.0.0.1 is just the loopback address to your computer, and the other address is reserved for local networks to identify each other internally.  Neither of them is your external IP address from your ISP.

I agree completely with NIC on his assesment. I would also like to add that if you are using Chrome, Firefox, IE or literally any browser, you are sending information about yourself and your computer such as OS Version, Resolution, IP Address and what browser you are using.
 
There are several ways to combat this such as using a proxy service, using a VPN Service or the easiest of them all, changing to a secure Web Browser.
Below are several browsers that block all this information, basically making your surfing invisible to the end server. There are limits to this in that it might block some access to sites due to them requiring this information or the need for cookies, but in general it will work well for you.
My personal favorite of the bunch is TOR. It is based off the Firefox kernel and works well. It also allows all the Firefox addons available.
https://www.torproject.org/projects/torbrowser.html.en
https://www.epicbrowser.com/
https://www.comodo.com/home/browsers-toolbars/browser.php (Comodo Dragon is based on Chrome)
https://www.comodo.com/home/browsers-toolbars/icedragon-browser.php (Ice Dragon is based on Firefox)
 
All of these browser will work well and should prevent you from broadcastion that information everytime you surf.
 
All this is assuming it is a browser broadcasting this information and not some malware that is broadcasting it. Ether way I would strongly recommend a through complete scan with an up-to-date antivirus scan.
 
Any question please let me know and good luck.

Hello, my name is Cindy.
 
May I suggest an app called CyberGhostVPN (CGVPN). Each time you sign onto a browser CGVPN gives you a different IP address, located anywhere around the world or just the United States, your choice.  It gives you complete anonumity.  You are given a different IP address each time you go online.  I love it!
I bank online. My bank called me recently to ask if I had been traveling across country (USA) in one day.  They had detected my sign-on from the east coast and the west coast in one day. I told them that I have an app that gives me anonumity on my browser.  That is what the VPN stands for (Virtual Private Network). Check it out on cyberghostvpn.com.  It's especially great for mobile devices (smartphones).

Hi Cindy
 
Agreed that whilst VPN is a great way to handle this it is in some cases beyond the capabilities of some user to use it and also it is a nono re. some ISPs (for only reaosns that they know).  Also, some websites will be off limits to you if for instances yo are phycically in the country that the website is hosted from but the VPN gives the impression that you are elsewhere and the website policy is that it only caters for userr in the same country as it is in...a case of being hoisted by ones own petard.
 
So for joe public I agree with bsodcsi...the best approach IMHO is a secure or hardened browser...but of course, if one can use and live with VPN then so much the btter.  I do for work but not for my private connection to the web...for that I have hardened/secure browsers.
 
Regards, Baldrick