Character controller going through walls?

I have a character controller that allows the user to fly around, however the player can move through walls even though I have a collider attached to the player. Would anyone happen to know what the problem is and how to mend it? Thanks for any help! Here is my code:

using UnityEngine;
using System.Collections;

public class FlyCam : MonoBehaviour
{


    public float mainSpeed = 10f; // Regular speed.
    public float shiftAdd = 25f;  // Multiplied by how long shift is held.  Basically running.
    public float maxShift = 100f; // Maximum speed when holding shift.
    float camSens = .35f;  // Camera sensitivity by mouse input.
    private Vector3 lastMouse = new Vector3(Screen.width / 2, Screen.height / 2, 0); // Kind of in the middle of the screen, rather than at the top (play).
    private float totalRun = 1.0f;

    void Update()
    {

        // Mouse input.
        lastMouse = Input.mousePosition - lastMouse;
        lastMouse = new Vector3(-lastMouse.y * camSens, lastMouse.x * camSens, 0);
        lastMouse = new Vector3(transform.eulerAngles.x + lastMouse.x, transform.eulerAngles.y + lastMouse.y, 0);
        transform.eulerAngles = lastMouse;
        lastMouse = Input.mousePosition;

        // Keyboard commands.
        Vector3 p = getDirection();
        if (Input.GetKey(KeyCode.LeftShift))
        {
            totalRun += Time.deltaTime;
            p = p * totalRun * shiftAdd;
            p.x = Mathf.Clamp(p.x, -maxShift, maxShift);
            p.y = Mathf.Clamp(p.y, -maxShift, maxShift);
            p.z = Mathf.Clamp(p.z, -maxShift, maxShift);
        }
        else
        {
            totalRun = Mathf.Clamp(totalRun * 0.5f, 1f, 1000f);
            p = p * mainSpeed;
        }

        p = p * Time.deltaTime;
        Vector3 newPosition = transform.position;
        if (Input.GetKey(KeyCode.V))
        { //If player wants to move on X and Z axis only
            transform.Translate(p);
            newPosition.x = transform.position.x;
            newPosition.z = transform.position.z;
            transform.position = newPosition;
        }
        else
        {
            transform.Translate(p);
        }

    }

    private Vector3 getDirection()
    {
        Vector3 p_Velocity = new Vector3();
        if (Input.GetKey(KeyCode.W))
        {
            p_Velocity += new Vector3(0, 0, 1);
        }
        if (Input.GetKey(KeyCode.S))
        {
            p_Velocity += new Vector3(0, 0, -1);
        }
        if (Input.GetKey(KeyCode.A))
        {
            p_Velocity += new Vector3(-1, 0, 0);
        }
        if (Input.GetKey(KeyCode.D))
        {
            p_Velocity += new Vector3(1, 0, 0);
        }
        if (Input.GetKey(KeyCode.R))
        {
            p_Velocity += new Vector3(0, 1, 0);
        }
        if (Input.GetKey(KeyCode.F))
        {
            p_Velocity += new Vector3(0, -1, 0);
        }
        return p_Velocity;
    }

    public void resetRotation(Vector3 lookAt)
    {
        transform.LookAt(lookAt);
    }
}

If you modify the transform position like that it will pass through anything if: a) You don’t include additional checks or b) use the character controller provided.