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I am sorry to hear of this difficult situation.
You are required to apply for EI within 4 weeks of losing your job or you may not be able to get any EI.
If you are denied EI you can appeal this but you will not likely win unfortunately as the law is very clear in this area.
I am sorry to have to provide this answer and suggest you call EI at once and explain the mistake and hope someone in authority shows compassion.