God certainly wants us to bring our concerns to Him privately. Jesus said, "When you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you" (Matthew 6:6).
However, the Bible also encourages us to pray for each other, and to ask others to pray for us. Paul, for example, repeatedly asked people to pray for him and his coworkers as they sought to tell others about the new life they could have in Christ. To the Christians in Thessalonica he wrote, "Finally, brothers, pray for us that the message of the Lord may spread rapidly and be honored, just as it was with you" (2 Thessalonians 3:1).
Remember: God loves us, and He is concerned about everything that concerns us. Furthermore, He has promised to hear our prayers when we come to Him sincerely and in faith, trusting Him to do what is best -- for us, and for those for whom we are praying. The Bible says, "This is the confidence we have in approaching God: that if we ask anything according to his will, he hears us" (1 John 5:14). This is possible because Jesus Christ has bridged the gap between God and us by becoming the final sacrifice for our sins.
Don't let your pride, or anything else keep you from asking others to pray for you -- because God is pleased when His people unite in prayer. And don't forget to pray for those who need your prayers -- whether they ask for them or not.