I think you can say the following:
I'm at the hospital, doing medical exams.
I'm at the hospital, undergoing medical exams.
I'm at the hospital, having medical exams.
I'm at the hospital, taking medical exams.
I'm not very sure if some of them may be confused with taking a written medical exam (you can't discard the possibility that someone could be at the hospital writing a exam).
Which of them is less ambiguous? Is there a better choice?