what type of visa were you earlier on ??? extending a tourist visa or a business visit visa doesnt need you to undergo a medical exam.

As far as i can understand from your question, you have come here on a family visit visa and now have got a job here and hence a visa from the employer.

You will need to go for the medical test again and then go ahead with the fingerprinting process. Take your last medical report with you (the bill); if it is less than 3 months since your last test they might let you off without the examination.