The one thing I am not hearing is if the OP has any interest with patient care? Many physicians that I know always wanted to be a doctor. Period. But of course many different paths one can take now in medicine and the combo program I posted before is one such program and I find it really interesting.
I agree that if your good in math and have the interest then follow the engineering program but apply to medical school. At my sons school all first year classes like Chem, physics, math and so on are taken by both LSA, engineering, pre med, etc. You will find out soon enough. My son used to tell me students would walk out of the first /second quiz /test muttering “I am not going to be a doctor or engineer”.
But for those that stayed and made it through they have wonderful careers to look forward to.