Yes you can get repair kits and there are literally hundreds of YouTube tutorials on how to do it. However I would not even attempt it. This is coming from someone who used to repair solid state electronics (TV and video cameras) for a living. It is possible to do, but I wouldn't do it myself. If the screen is working better sticking a screen protector over it, not for the device but for avoiding cut fingers and keeping the broken glass in place.

 

I broke the screen on my nexus 7(2013) and bought the replacement screen on eBay. It was a LCD+digitizer combo because they are bonded together on the nexus. I watched a video on YouTube and did it myself. Went perfectly. I had never done it before and had no trouble. But it is risky for sure. I've never done it on my s3, or watched any videos to know how hard it would be. But I personally wouldn't be able to resist trying. Lol.

 

If you decide to replace it yourself, be careful. I know several people who've ruined their digitizer. As mentioned above, there are several tutorials on YouTube. I suggest watching as many as you can to get an overall idea of the different steps people have taken when doing a replacement.