Draw path to follow with mouse problems

I need help with my code. So far, it works okay. The player follows the mouse path as expected, but the player moves at the same speed as how fast or how slow you drag the mouse. Please help! I need the player to move at a normal and controlled speed regardless of how fast or slow I drag the mouse. I'm posting my code here for a reference. Thank you.

 using UnityEngine;
 using System.Collections;
 
 public class FollowMousePath : MonoBehaviour {
 
     public float[] posXArray;
     public float[] posYArray;
 
     float startX;
     float startY;
 
     public float nextStepX;
     public float nextStepY;
     public float mySpeed = 45;
     public float recordTime;
 
     public Vector3 previousPos;
     public Vector3 mousePos;
     public Vector3 endPos;
 
     public int whichArrayToRecord;
     public int myMoves;
     public int maxMoves;
 
     public bool playerGo;
     public bool recordPos;
     public bool beginRecording;
 
     // Use this for initialization
     void Start () {
         posXArray = new float[300];
         posYArray = new float[300];
     }
     
     // Update is called once per frame
     void Update () {
 
         mousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
 
         if (Input.GetMouseButtonDown (0)) {
             beginRecording = true;
             recordTime = 0.0001f;
         }
 
         if (Input.GetMouseButtonUp (0)) {
             maxMoves = whichArrayToRecord;
             beginRecording = false;
             whichArrayToRecord = 0;
             playerGo = true;
             myMoves = myMoves + 1;
         }
 
         if (playerGo && myMoves < maxMoves) {
             nextStepX = posXArray[myMoves];
             nextStepY = posYArray[myMoves];
             transform.position = new Vector3(Mathf.MoveTowards(transform.position.x, nextStepX, mySpeed * Time.deltaTime),Mathf.MoveTowards(transform.position.y, nextStepY, mySpeed * Time.deltaTime), transform.position.z);
             myMoves += 1;
         }
 
         if (myMoves == maxMoves) {
             myMoves = 1;
             playerGo = false;
         }
         
         if (mousePos != previousPos && beginRecording) {
             previousPos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
             endPos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
             posXArray[whichArrayToRecord] = endPos.x;
             posYArray[whichArrayToRecord] = endPos.y;
             whichArrayToRecord +=1;
             recordTime = 0.0001f;
             recordPos = false;
         }
     
         if (recordPos && Input.GetMouseButtonUp(0)) {
             endPos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
             recordPos = false;
             playerGo = true;
         }
 
         if (endPos.z != 0)
             endPos.z = 0;
 
     }
 }