First, avoid spicy foods or any other foods that may trigger heartburn and avoid eating too much at one meal. Second, it is okay to take Tums while pregnant. Of course, confirm this with your doctor and do not take more than the reccommended dose. Finally, try drinking a glass of milk or yogurt to relieve heartburn.

I second milk, yogurt, or cottage cheese. These are good sources of calcium and are slightly basic (alkaline), so they are natural "buffers".

Foods such as citric fruits (lemons, oranges, etc.) and tomato-based products (marinara, salsa, etc) will also increase acidity in the stomach. Ask your doctor about ways to get the vitamins you're giving up by avoiding acidic foods. Some doctors will tell you about other foods and some will suggest vitamins. A great example of this would be to get the Vitamin C you miss out on, you can add more broccoli to your diet. (Also, vitamin C as a supplement may not make your stomach better because it is often in the form of ascorbic acid, so look for the "buffered" version which will be vitamin C with another mineral such as calcium or potassium.)