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);
     }
 }