Bug with collision detection with Tiled(LWJGL & Slick2D)

Newbie & Debugging Questions
#1

Information:
The tiled map and player : http://prntscr.com/2c445u . I tried to make some kind of pixel-precise movement
It is weird because I can achieve stuff like this sometimes : http://prntscr.com/2c44px

I can not figure out how to prevent these bugs…(It needs to works with more maps too…)I believe that the whole issue is caused by the way I calculate tileX and tileY (player’s positions @ grid. Is there a better way?)

This thing(in pic) only happens when I try to move left or right and I am in the middle of 2 tiles. Is there any way to prevent that?

(I am not a noob with java. Its just the fact that I am now taking my first steps in game-dev.)
Here is the full code:

//packet
//imports
public class LevelOne extends BasicGameState{

public int state;
boolean esc;
Input input;

private TiledMap map;

private float x,y,vel;


public LevelOne(int state){
    this.state = state;
}

@Override
public void init(GameContainer arg0, StateBasedGame arg1)
        throws SlickException {
      esc = false;
      map = new TiledMap("res/map/map.tmx");

      x = 2 * 32;
      y = 1 * 32;
      vel = .1f;
}

@Override
public void render(GameContainer arg0, StateBasedGame arg1, Graphics g)
        throws SlickException {
        map.render(0, 0);

        g.fillRect(x, y, 32, 32);

}

@Override
public void update(GameContainer gc, StateBasedGame sbg, int delta)
        throws SlickException {
    input = gc.getInput();
    if(esc){
        Mouse.setGrabbed(false);

    }else{
        Mouse.setGrabbed(true);
    }
        if(input.isKeyPressed(Input.KEY_ESCAPE)){
            esc = true;
        }   
    if(esc){
        Mouse.setGrabbed(false);
            if(input.isKeyPressed(Input.KEY_R)){
                esc = false;
            }else if(input.isKeyPressed(Keyboard.KEY_Q)){
                System.exit(0);
            }else if(input.isKeyPressed(Keyboard.KEY_M)){
                esc = false;
                sbg.enterState(0);
                Mouse.setGrabbed(false);
            }
        }

    int objLayer = map.getLayerIndex("Objects");

    int tileX = (int)(x + 1)/ 32; 
    int tileY = (int)(y + 1)/ 32;

    System.out.println(tileX +"   "+ tileY);

    //TODO -- FIX COLLISIONS

    if(input.isKeyDown(Input.KEY_RIGHT)){
        if(map.getTileId(tileX+1, tileY, objLayer) == 0){
            x+= vel * delta;
        }
    }

    if(input.isKeyDown(Input.KEY_LEFT)){

        tileX++;

        if(map.getTileId(tileX-1, tileY, objLayer) == 0){
            x-= vel * delta;
        }

        tileX--;

    }

    if(input.isKeyDown(Input.KEY_UP)){

        tileY++;

        if(map.getTileId(tileX, tileY-1, objLayer) == 0){
            y-= vel * delta;
        }

        tileY--;

    }

    if(input.isKeyDown(Input.KEY_DOWN)){
        if(map.getTileId(tileX, tileY+1, objLayer) == 0){
            y += vel * delta;
        }
    }

        }

@Override
public int getID() {
    return state;
}
}

Thanks in advance