God does care about us - far more than we will ever imagine. Even when we forget Him or ignore Him, He does not forget us or ignore us, because His love for us is everlasting. The Bible says, "Give thanks to the Lord, for he is good; his love endures forever" (Psalm 106:1).
Why, then, doesn't He take our problems away when we ask Him? I've pondered this question most of my life, and to be honest I don't have an answer that covers every situation. God sees the whole picture; we see only a part. Someday we will understand, when we see Jesus in heaven - but until then, the Bible says, "We live by faith, not by sight" (2 Corinthians 5:7).
But I do know this: Often God answers our prayers not by taking our problems away, but by giving us the strength and wisdom to deal with them. Yes, when problems arise we all wish they'd just go away - but sometimes God wants us to turn to Him and instead ask Him for the strength to stand up under them. And when we do, He has promised to grant it. The Apostle Paul said, "I can do everything through him (Christ) who gives me strength" (Philippians 4:13).
May this be your experience as you turn your life over to Jesus Christ and trust your problems into His care. God loves you; He loves you so much that He sent His Son into the world to make you part of His family forever. Put your trust in Him today.