Chest pain is a fairly common symptom. There are many potential causes for the pain, some of which are serious and some of which are minor. As you rightly point out, the concern is if this is coming from your heart. While unlikely, this would be life threatening and therefore I believe you need to see your primary care doctor
to discuss this and have it ruled out. Your primary care doctor can provide you with more information about different causes of the pain.
Angina, is chest pain (or other symptoms) caused by a relative decreased amount of blood to the heart. While it would be unusual in a 28 year old women, it is possible and would indicate you are at risk of a heart attack. This should be evaluated.
Other causes of chest pain exist. Anxiety
is a very common cause. A panic attack classically includes symptoms of shortness of breath and chest pain. Another common cause is gastrointestinal distress. This includes esophageal spasm and gastric reflux.
Your symptoms sounds like what we call costochondritis. This is inflammation in the rib muscles that causes sharp pain. This inflammation is difficult to heal as the ribs keep moving with each breath.
Talk to your doctor. There are diagnostic and treatment options that you have and would require.