Can't move and fire at the same time!

So I am making a 2d infinite runner which requires moving up and down by pressing the left side of the screen and shooting by pressing the right. I have the player moving up and down by tapping the corresponding half (the top or bottom of the left side) or dragging (haven't started this). But when I tap the right the ship stops. This doesn't happen in PC mode but does on mobile, I've been stuck on this for a while so if anyone can help I'd greatly appreciate it.

 //Touch Controller Script
 
 public class touchControls : MonoBehaviour {
 
     public playerManager player;
     float middleScreen = Screen.height / 2; 
     float thirdScreen = Screen.width / 3;
     Touch myTouch;
     Touch mySecondTouch;
 
     void Start(){
         Input.simulateMouseWithTouches = true;
         Debug.Log ("middle " +middleScreen);
     }
 
     void Update(){
 
 
 
         if (Input.touchCount > 0) {
             if (Input.GetTouch (0).phase == TouchPhase.Began) {
                 myTouch = Input.GetTouch (0);
 
                 if (myTouch.position.y > middleScreen) {
                     if (myTouch.position.x < thirdScreen) {
                         moveUp ();
                     }
                 } else if (myTouch.position.y < middleScreen) {
                     if (myTouch.position.x < thirdScreen) {
                         moveDown ();
                     }
                 }
             } else if (Input.GetTouch (0).phase == TouchPhase.Ended) {
                 noPress ();
             } else if (Input.GetTouch (0).phase == TouchPhase.Canceled) {
                 noPress ();
             }
     }
 }

Player Manager

     //shoot linked to event handler (invisible button)
     
     public class playerManager : MonoBehaviour {
     
         public float speed = 15;
         public GameObject bullet;
         public Transform firePoint;
         public bool canFire = true;
         public static float fireRate = 0.3f;
     
     public void shoot (){
             
         if (canFire == true) {
                 StartCoroutine (shootNow ());
             
             }  
     
         
         }
     
         public IEnumerator shootNow(){
             canFire = false;
             //Debug.Log ("firing");
             Instantiate(bullet, firePoint.position, firePoint.rotation);
             yield return new WaitForSeconds(fireRate);
             canFire = true;
     
         }
     }
     
     

Also if you could point my in the right direction to dragging touch controls that would be awesome :D