Would my stomach skin tighten up on its own when going on my diet to lose 20 lbs?

Yes: If you lose fat under the abdominal wall, you should be palpating abdominal wall skin and muscle and abdominal contents only. If his is the case you may feel your abdomen tightened up. You might also carried out abdominal muscle exercises such as push ups with your face down or lifting head up while lying down on your back. These exercise should strengthen and tighten up our abdominal wall muscles