Is heart attack chest pain typically a deep feeling in the chest or closer to the surface?

Usually deep. But there is not an answer that fits every occurrence. Cardiac chest pain is usually dull ache or squeezing sensation beneath the breastbone, sometimes with radiation to the jaw, shoulder or arm, usually the left--most often with exercise or stress.
Dull. Typical pain is a pressure or heaviness, tightness sensation. However patient's perception of pain is different.
Can be either. Chest pain with a heart attack comes from the damaged tissue causing irritation of the tissue around it. Shoulder and arm pain are from irritation of the diaphragm, chest pain from irritation of the chest wall, etc. The location of the pain depends on the location of the inflammation.

Related Questions

To have a heart attack you do not have to have chest pain. Can you have a heart attack while just feeling skipped beats as the only symptom?

Unlikely. Hi MoeA645, Yes, many people who have heart attacks do not suffer the typical symptoms of chest pain, difficulty breathing, nausea & sweating. Still, it's very unlikely feeling just a few skipped beats means you are having a heart attack. You may have something called palpitations, which are often nothing to worry about. If the skipped beats occur often or with other symptoms, I'd see a doctor. Read more...

Are all types of chest pain a heart attack?

No. There are many organs and structures that live in the heart's neighborhood! any of these can cause chest pain. These include esophageal and stomach problems (like reflux) and lung problems. Any problems of the chest wall muscles or nerves (like a case of shingles) can cause chest pain. Even the joints along the sternum can become inflamed and cause chest pain, a problem known as costrochondritis. Read more...
No. Although angina pectoris gets the most attention, the list also includes esophageal reflux, pericarditis, pinched nerve in the thoracic spine, pleuritis, costochondritis, and a number of other things. Your doctor should be able to sort this out with a thorough history, physical exam, and simple testing. Read more...