God urges us not only to pray and commit our burdens to Him, but to seek out others who will help us carry our burdens by their prayers. The Bible says, "Carry each other's burdens, and in this way you will fulfill the law of Christ" (Galatians 6:2).
This is why we shouldn't hesitate to ask others to pray for us. God loves us, and one of the ways He shows His love to us is by promising to hear us when we pray. God sent His Son into the world so that the barrier separating us from God -- a barrier caused by our sin -- could be destroyed. Because Christ gave His life for us, the Bible says "we have gained access by faith into this grace in which we now stand" (Romans 5:2).
Does this mean we should indiscriminately ask everyone we know to pray for us, no matter how personal or delicate the situation might be? This may be appropriate at times -- but not always. Sometimes our burdens shouldn't be widely shared, because people who don't know us may not be able to pray intelligently. Jesus prayed with His disciples -- but frequently He also prayed alone, because even His closest disciples couldn't have understood the burdens He was carrying.
Don't let your pride, or anything else, keep you from asking others to pray for you. Prayer is one of our greatest privileges, and the Bible's promise is true: "If we ask anything according to his will, he hears us" (1 John 5:14).