Our family has some very serious financial needs, but I grew up thinking we aren't supposed to pray about problems like this, because they're selfish, and God doesn't answer self-centered prayers. Am I wrong?
Yes, you are wrong. Because God loves us, He is concerned about everything that concerns us. If you grew up going to church, perhaps you said the Lord’s Prayer every week, and in it Jesus told us to pray for the things we need: “Give us this day our daily bread” (Matthew 6:11, KJV).
Think of it this way. I see from your letter that you have two children. If one of them came to you with a scraped knee, would you refuse to wash and bandage it? If they were hungry and wanted something to eat, would you tell them you couldn’t be bothered because they were just being selfish? Of course not. You love your children and would do everything you could to meet their legitimate needs.
The same is true with God. God loves us so much that He was willing to come down from heaven in the person of His Son, Jesus Christ, and give His life for our salvation. If God loves you that much, don’t you think you can bring your needs to Him in prayer? Jesus said, “If you… know how to give good gifts to your children, how much more will your Father in heaven give good gifts to those who ask him!” (Matthew 7:11).
Make sure of your commitment to Christ. Then ask Him for practical wisdom to deal with your financial problems. You can trust His promise: “God will meet all your needs according to the riches of his glory in Christ Jesus” (Philippians 4:19).