Problem with dragging objects

I have following script for dragging things:

 using UnityEngine;
 using System.Collections;
 
 public class DragTile : MonoBehaviour {
 //declaring some variables
     private bool mousedwn;
     
     
     void OnMouseDown() {
         if (!GameData.freemove){
             mousedwn = true;
         }
     }
     void OnMouseUp() {
         mousedwn = false;
     }
     // Update is called once per frame
     void Update () {
         if ((mousedwn) && (Input.GetMouseButtonDown(0))){
             this.transform.Translate(Input.GetAxis("Mouse X"),0,Input.GetAxis("Mouse Y"),Space.World);
         }
     }
 }

However it doesn't work as planned. It works fine if I change

 if ((mousedwn) && (Input.GetMouseButtonDown(0)))

into

 if (mousedwn)

but then I can't tell the difference between buttons. How can I fix it?