Touch Input, user can touch across the screen, not wanted

Hey !

I'm making a game where the user can move the character by holding down a finger on the screen and move it horizontally, and then the character is moving on the x-axis, so the y- locked.

The game is 2D, and its mechanic is to evade game objects. The user gets the option to move the character freely on the x-axis, but I don't want the players to cheat by for example clicking at 500 units(x-axis) from 0 units, I want to force the player to drag the character around instead of clicking. The game is developed for Android.

Sorry for my shitty explaination, but I need you guys help.

Code:

 if(Input.touchCount > 0 && Input.GetTouch(0).phase == TouchPhase.Moved /*&& touchPosition.x < (transform.position.x + 1f) && touchPosition.x > (transform.position.x - 1f)*/)
             {
                 ChangePosition();
             }

ChangePosition method:

 void ChangePosition()
     {
         fingerPos = Camera.main.ScreenToWorldPoint(new Vector3(Input.GetTouch(0).position.x, 450, 5f));
         transform.position = fingerPos;
     }