Can I be close to God without all the fear?
Yes. In fact, you were never meant to carry that fear at all.
There is a kind of religion that puts a whip in God's hand, but that is a human shadow cast over the face of Love, not the Father Jesus revealed. Hear how plainly he speaks: "There is no fear in love; but perfect love casteth out fear: because fear hath torment. He that feareth is not made perfect in love" (1 John 4:18, KJV). Fear and closeness to God cannot occupy the same room; where one enters, the other leaves.
When you come near, you are not approaching a judge waiting to condemn but a Father running to meet you, as in the story of the son who returned and was embraced before he could even finish his apology (Luke 15:20, KJV). Jesus said, "Fear not, little flock; for it is your Father's good pleasure to give you the kingdom" (Luke 12:32, KJV). That is God's disposition toward you: good pleasure, not wrath.
If certain scriptures thunder with terror, remember that those are the marks of a people still perceiving God dimly, through their own dread. Jesus corrected such readings again and again, saying "Ye have heard that it was said... but I say unto you" (Matthew 5:43-44, KJV). He read every old word through the Father he knew, and so may you.
And the Kingdom is not a distant reward to be feared into earning. It "is within you" (Luke 17:21, KJV), and again, "the kingdom of the Father is spread out upon the earth, and men do not see it" (Gospel of Thomas 51.16-18). Closeness, then, is not a border you cross under threat; it is a truth you awaken to. In the quiet beneath your fearful thoughts, you will find you were never separate at all.
Let the fear go, gently. What remains when it leaves is God.