Why does the little piece of skin that is underneath my tongue hurt? it feels rugged and sore. it hurts to move my tongue around and feels tight

Ulcer most likely: Oral (apthus) ulcers can be very painful. The good news is they usually resolve on their own in 10-14 days. In the mean time stay away from spicy and acidic foods, as they can make it hurt more. Rinse with warm salt water to keep area clean. For pain pick up some oragel with Benzocaine at drug store. If condition worsens see your dentist for an evaluation.

Sore frenum: This muscle is the lingual frenum. It is often ulcerated by rubbing the bottom of the tongue over the edges of the lower incisors extensively. A common activity which produces this effect is oral sex. Try a few days of resting it and it should go away. If it doesn't go away in a week, please see your dentist.

Lingual Frenum: In your case the lingual frenum is the problem, based on the picture. It can be irritated by tongue motion in general. It can be treated very easily. See an ENT doc.