We don't ask people to pray for us because they're better than we are, or because God might be more likely to listen to them. We ask them to pray for us simply because we know we are in need, and that God is pleased when we pray for others.
I often think of the Apostle Paul in this connection. He was the greatest follower of Jesus Christ who ever lived, and if anyone might have felt he didn't need others to pray for him, it would've been Paul. But repeatedly he asked people to pray for him -- just as he was praying for them. He wrote, "Brothers, pray for us that the message of the Lord may spread rapidly" (2 Thessalonians 3:1). If Paul sought the prayers of others, shouldn't you also?
If someone isn't trustworthy, of course, you shouldn't share your problems with them. But don't let your pride, or anything else, keep you from asking for the prayers of those who love Christ and care about you. And don't forget to pray yourself, both for your own needs and the needs of others. The Bible says, "Serve one another in love" -- and one way we do this is by praying for them (Galatians 5:13).
Never forget: One of our greatest privileges if we know Christ is the privilege of prayer, and it is ours because He opened heaven's door by His death and resurrection for us. Make sure of your commitment to Christ, and then bring your every concern to Him in prayer.