You can apply for Employment Insurance (EI) if you have worked enough hours and have a valid work permit and/or implied status. Receiving EI will not affect your ability to apply for permanent residency in the future.
Sometimes migrant care workers are denied or told that we are not eligible for EI because of our work permit. This is not true. You are entitled to this benefit. All migrant workers deserve access to benefits and income supports regardless of immigration status.