Dear kiwibearjen:
As far as I can tell, Calc II is not necessary for admittance into medical schools (please keep in mind that I have only looked at state schools, I'm not sure about the private medical schools around the country and how or if their admission requirements differ). However, Physics with Calculus, as far as I can tell, is "recommended", and at most schools I've looked at (due to transferring out of Florida in the next year) many second semester Physics with Calculus courses require Calc II as a co/pre-requisite. This probably differs between each and every school, but it has been a theme at the ones I've been looking into. Maybe this is what your counselor was trying to get at? I'm not a math person either, so I'm trying to figure how I can get around taking Calc II but I doubt I'll be able to do so. Best of luck to you in both your medical and mathematical pursuits. Also, welcome to SDN...