Yes. You are feeling correctly. This is how a person responds to a situation in which they are thrown in the deep end and made to feel like a fraud for not already knowing how to swim. These are the CORRECT FEELINGS, I cannot stress that enough. My advice, from my experience: acknowledge your feelings are well-founded and valid; treat school not only as a means to learn about the subject you're studying, but about how to be strong in a very tenuous position; eat and sleep as well as you can; investigate talk therapy options.
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You are doing a great job, I promise.