The Bible argues with God more than most sermons do
If anger at God were off-limits, someone forgot to remove it from Scripture. The Psalms ask how long God intends to keep forgetting, and whether he plans to hide his face indefinitely. Job says plainly that he will not restrain his mouth, and that he intends to complain in the bitterness of his soul. Lamentations accuses God directly of the ruin the writer is living in.
These are not the villains of the text. They are the people the tradition preserved, quoted, and set to music. Whatever else that means, it means the anger was not considered too dangerous to write down.
Jesus himself, on the cross, quotes the opening line of Psalm 22 - the question of why God has abandoned him. If that sentence can be said there, it is difficult to argue it must never be said anywhere.
Anger and unbelief are not the same thing
Much of the guilt around this comes from collapsing two different things into one. Anger at God assumes God is there. It is a complaint addressed to someone. Indifference does not bother complaining.
The people in Scripture who shout at God are, without exception, people still in the conversation. Psalm 13 opens with four accusations and closes with the writer still speaking to the same God he was just accusing. That is not the shape of someone walking away. It is the shape of someone refusing to.
This matters practically. If you have been treating your anger as evidence that your faith has failed, you may have the sign backwards. The person who has genuinely stopped believing does not usually lie awake furious about it.
What anger is often carrying
Anger at God rarely arrives on its own. Underneath it there is usually a specific loss, an unanswered prayer, a person who was not healed, a situation that did not turn, or an injustice nobody was held to account for. The anger is frequently the only part that can be said out loud.
It is worth naming the actual thing. Not the theological version - the specific one. "I am angry that she died and nobody explained it" is a different sentence from "I have doubts," and it is the one that can actually be prayed.
This is also where the honest limit sits. Scripture does not, in most of these passages, resolve the complaint. Psalm 88 ends in darkness with no turn toward comfort. Job gets an answer that is not really an answer to the question he asked. Anyone who tells you the Bible always ties this off neatly has not read the bleaker parts of it.
One honest next step
Say the angry sentence as a prayer, in the words you would actually use, without cleaning it up first. Not a polite paraphrase - the real one. The Psalms give ample precedent for the unedited version, and a prayer you have sanded smooth is usually a prayer about something else.
If the anger is tangled with grief, trauma, or something done to you by a person in a church, that is worth taking to a counsellor or a trusted pastor as well as to prayer. Some of what gets called anger at God turns out, on closer inspection, to be anger at someone who claimed to speak for him. Those need untangling, and that is human work, not something to sort out alone.