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Further to your question I am an immigration solicitor and will be assisting you with your question today
Can you please confirm who your sponsor is?
You can apply to extend your student visa or you can apply for either the Graduate route or the Careworker visa
Yes, you could find a job in the NHS and get them to give you a certificate of Sponsorship which will allow you to apply under the Careworker visa.
Please find enclosed the guidance