Is it possible for the muscles in your chest to tense up and spasm during panic attacks?

Absolutely. People with panic attacks have a variety of symptoms that they often misinterpret at evidence they are dying--can't catch their breath, have chest pain, feel dizzy and about to faint. Fortunately, the symptoms are not dangerous, even though they feel that way. Treatment is available and well worth seeking out.
Chest muscles/Panic. Sure, result of increased adrenaline which tightens blood vessels & shifts glucose supply to muscles. Refer to my previous answers for details.
Yes. A panic attack is a fight or flight reaction to a situation or to nothing. That reaction involves all muscles tensing in preparation for fighting or running, including your chest muscles.