I'm a very anxious person. Had panic disorder. Could the reason of anxiety be mitral valve prolapse? Could it get better with medication?

Anxiety treatment. Anxiety and panic can easily go together, and some have also noted that mitral valve prolapse (mvp) and panic disorder can happen in the same patient. But that doesn't mean that mvp causes the panic. In most people, mvp causes no symptoms or physiological problems. Regardless, medications like ssri's can treat the anxiety & panic, along with psychotherapy. See your doctor for evaluation & help.
Absolutely. Anxiety is very common. Stress, medical conditions are common triggers for anxiety. Lots of treatment available (medical, psychological, spiritual, etc) talk to your doctor.
Probably not. Mitral valve prolapse does not cause anxiety. There are several antidepressant medication that are fda approved for anxiety/panic disorders. These can be very effective. You should discuss options with you physician. I have found zoloft (sertraline) to be particularly beneficial in panic disorder.