Switch/Case function with tilt switch and RGB

I don't think your sketch is going to do what you expect, remember loop() loops continuously.
So let's say the tiltState is HIGH what is your code going to do first time round the loop?
What happens the next time round the loop if tiltState stays HIGH?
What happens if tiltState goes low and stays that way?

Start small and build your program up gradually, put in print statements so that you can see what it is doing and why.
Just try reading and printing the switch state to start.