Yes, you should. The Christian's needs are indeed God's concern; not even the smallest detail escapes His notice. However, He tells His people to imitate Jesus: "they should not merely look out for [their] own personal interests, but also for the interests of others." (Philippians 2:4).
Selfless prayer, though, isn't natural to us. We too easily think of God as a "genie", someone to do our bidding as we live life our own way. Thankfully, God has supplied a Helper. The Holy Spirit, our willing and able partner in praying effectively, intercedes for us when we can't pray as we should. (Romans 8:26).
How should we cooperate with the Spirit's intercession for us? First, we must recognize God's authority, holiness, and glory. Then, we need to submit our lives to his leadership. When we do, God?s will and desires become foremost in importance for us. Finally, we must submit our future to Him, trusting that He will bring great good out of negative as well as positive events in our lives.
In submission to the Lord, we will discover greater peace and joy. We'll also find new words for our prayers. Even more importantly, we will develop a deeper understanding of God's greatness.