If God were just like we are (only somewhat bigger), then you might be right. After all, you and I are limited, and it's easy for us to think that God must be limited also.
But God isn't limited! We are finite, but He is infinite. We are limited, but He is unlimited. We occupy only one small corner of the universe, but He is everywhere. And no matter how much we think we know, our knowledge is still very small, like one grain of sand on the seashore, but His is complete and total. The Psalmist exclaimed, "How great are your works, Lord, how profound your thoughts!" (Psalm 92:5).
But something else about God is infinite -- and that is His love. If God didn't love us, we wouldn't have any reason to think He is concerned about us or hears our prayers. But He does love us, and the proof is that He sent His only Son into the world to save us. Jesus did this by giving His life for us on the cross. Have you committed your life to Him?
Don't worry about God losing track of your prayers; He won't. God is far greater than that, and you can trust His promise to hear your prayers and answer them according to His will. In fact, God delights in our prayers, just as parents delight in their child's words. 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).