Okay, it's solved... kind of. The reinstall repaired most of the crashes but it still kept crashing saying that same Java crash thing as previously. I found out that only way to run it is to use HD 4600 OR right click Minecraft icon and choose GTX graphics every single time I start Minecraft. If I don't choose it, the game tries to use HD 4600 and surprise, it lags badly. If I force GTX from Nvidia control panel, it crashes every time. If I use automatic graphics, it'll use HD 4600 even though it says it's going to use GTX.
So if someone is having the same problem after GTX drivers update, try right click Minecraft and run with GTX graphics, it works for me now.