Big Duke 6-
It's been decades since I flew anything with carb heat or manifold pressure. And, I don't know what a 'wind factor' is...
However, I do fly in comparable terrain, frequently, whether that's mountainous or not. I can relate to your story.
Thoughts-
Helicopters shake/vibrate more with increased speed, have your instructor demonstrate this and you'll be more comfortable.
Turbulence is usually temporary. Do the usual stuff to hold altitude in whatever you're flying when you hit the bumps. In a few seconds, you'll probably be in some air going the other direction to what you're fighting now. Don't take any hazard lightly in the meantime.
Your initial impulse to slow down was correct, but don't be excessive, too slow has it's own hazards. If terrain is a concern, you don't want to be slower than best climb.
You don't mention altering course. I'm a big believer in going around trouble, I'll divert/turn away from anything that implies it will exciting or hard work.
I do wonder why you're not talking with your instructor about this? That should be your best source of local knowledge, you, the aircraft, and weather.