Please what visa procedure is fast to process since there is urgency in this case.

Tijjani， S2 type is fine. You need to get an invitation letter from that hospital is required. The process is as usual. You need to make an appointment and then submit your applications on the appointed date. If you get through the interview, you will be informed when to pick up your application.

Since your case is really urgent, I think you should contact the embassy and ask if they can deal with your case in a special way.
Tel: 09-4604708

If you they don't receive the phone calls, then I think you should visit the embassy in person.