Why can't I just believe what makes me happy?

Because if the things that make you happy are wrong and there really is a hell, you will spend more time unhappy on the eternal scale of "time".

Because what makes you happy might make others unhappy. What do you do then? Who's happiness is more important? Your happiness shouldn't trump the happiness of the most important person (Jesus). Everything you do should be to make God happy. If you become happy though this, that is a nice bonus. In fact, God's happiness will lead to the most joy in His followers, which means the most joy out of everyone (believer or not).

Psalm 4:7 You have put more joy in my heart than they have when their grain and wine abound.

Psalm 16:11 You make known to me the path of life; in your presence there is fullness of joy; at your right hand are pleasures forevermore.

Psalm 30:4-5 Sing praises to the LORD, O you his saints, and give thanks to his holy name. (5) For his anger is but for a moment, and his favor is for a lifetime. Weeping may tarry for the night, but joy comes with the morning.

There seems to be a paradox: sacrifice happiness to receive more happiness? But if you notice from the last Psalm referenced, perfect joy is not guaranteed here and now. Psalm 16 shows that we receive our "fullness" of joy in the presence of God. Eternity. Heaven. Fullness of joy.