If I have indigestion, should I be concerned for myself or my baby?

No. Mild to moderate indigestion is common in pregnancy because of the hormones of pregnancy and the pressure on the stomach from the growing uterus. Avoid fatty foods. Avoid onions, tomatoes and garlic. Allow at least three to four hours between your last meal for the night and when you go to bed.
Yes and no. Plenty of people suffer from heartburn. As long as you can manage it you should be fine. Make sure with your doctor you don't have h pylori and chronic heart burn can cause long term damage, so you need to learn what to eat and what to avoid. Your baby should not be affected. If you are pregnant, then indigestion is common during this time and will pass after you deliver and will not affect baby.