If its so wrong to show off and want praise, How come Hashem wants us to praise Him so much through tefilla and Tehillim (prayer & Psalms)?

You are correct , that God is Perfect, and accordingly all of the mitzvot (commandments), just as all of the praise, is not for His sake, but for us. He obviously doesn't need our praise, but it's great for us (even if we can describe just a small part of His greatness) to strengthen our motivation to imitate Him and follow His advise and directives. It helps us be in awe and love of His Greatness to want to be like Him, and most important helps us define and identify what are those traits that we want to emulate in Him. It also helps our relationship with Him (like a parent hangs his young child's pictures on the refrigerator to make him feel good).