I'm doing a formal writing essay and I'm using a phrase from an online source. The phrase is:
What is an alternative, more formal term I could use?
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Fix your "your/you are" mistake and do not use contractions in formal writing.
The answer to your question depends on how strong your statement needs to be. You could use a mild version You are in trouble, or possibly you are out of options now. The already suggested you are doomed is a bit more dramatic. As a threat, it could be replaced by you are finished.
That really depends on the context, and how the individual is 'screwed'. We can't tell you what word or phrase best replaces it, because this is not the place for writing advice, but we can give you some suggestions.
In the case that this person is 'screwed' because their plans haven't gone the way they want, or in the case that some fatal flaw has ruined their plans, you could say "you have been undone" or "you are ruined" to express that idea.
There is a problem with each one though; the former is a polite way of saying their plans have been actively defeated, while the latter suggests a general loss on the person, but could be a bit excessive for what you're looking for. So make sure you use these in the right context.
In addition to the other suggestions, here are some alternatives in an approximate order of more formal -> less formal, at least by my reading
"In serious trouble" is a bit wordy, but gets the point across without breaking formality. "Doomed" might also work if you believe that there is well and truly no good way out of the subject's predicament.
If the goal of the statement includes humor, then you could try understatement by using something like "in a bit of a spot".