I want to know if I can find a shiny at any point of the game.
Yes, Shiny Pokemon can be found anywhere where you can find wild Pokemon. No Pokemon are immune to apperaing shiny, and none have more chance. However, Shiny Pokemon aren't a common as they may seem - there is a 1/8192 chance of one appearing and I've never seen more than ten...
The only way to increase the chance of a Shiny Pokemon appearing is using "Masuda Method".