Every time I eat meat or eggs I end up with chest pains. Why?

Low Hydrochloric acid is most likely the reason for these pains, taking a shot of apple cider vinegar a few minutes before a high protein meal can help with digesting the meats. Digestive enzymes in fermented foods like beet kvass, pickled vegetables, sauerkraut help with breaking down foods and aid digestion.
Also notice if you get any pain, discomfort, gas, brain fog, "hungover feeling" with eggs and any other foods. Meat, eggs and many vegetables are high on sulfur and can be an issue when not metabolized properly in the body.

If the stomach does not have sufficient levels of hydrochloric acid, the proteins in animal products can be very difficult to break down. A simple home test is to mix 1/4 teaspoon of baking soda in 1/4 cup water and drink it down. Have a timer ready and start it as soon as you drink it down. If it creates a burp under 3 minutes, this can be a sign that there is ample HCl. There are many other body signals that can help you determine this, as well but might be a start in finding the source of discomfort.

Have checked into your overall digestion - gallbladder, intestinal issues. It could also be a food intolerance which is causing the "heartburn" symptoms.

Possibly you are experiencing a reaction to those foods. Maybe you have food sensitivities.