Camera shaking and barely moving after adding a clamp to x rotation?

using UnityEngine;
using System.Collections;

public class CameraController : MonoBehaviour {

	public int Sensitivity;
	private float MouseYSet;

	void Start () {
		MouseYSet = Input.mousePosition.y;
	}

	void Update () {
		transform.localRotation = Quaternion.Euler (Mathf.Clamp (transform.rotation.x, -90, 90), 0, 0);

		if (Input.mousePosition.y > MouseYSet)
		{
			transform.Rotate (new Vector3 (-1, 0, 0) * (Input.mousePosition.y - MouseYSet) * Sensitivity * 10 * Time.deltaTime);
			MouseYSet = Input.mousePosition.y;
		}
		if (Input.mousePosition.y < MouseYSet)
		{
			transform.Rotate (new Vector3 (-1, 0, 0) * (Input.mousePosition.y - MouseYSet) * Sensitivity * 10 * Time.deltaTime);
			MouseYSet = Input.mousePosition.y;
		}
	}
}

you are better to use Input.GetAxisRaw() Instead.

replace your Update() function with this:

float y = 0f;
void Update(){
	y-=Input.GetAxisRaw ("Mouse Y") * Sensitivity * 10 * Time.deltaTime;
    y=Mathf.Clamp (y, -90, 90);
	transform.rotation = Quaternion.Euler(y, 0, 0);
}

I didn’t test the code. but hope it will help

Still shaking!