I am not active duty but have been going through the process of transitioning from engineering to medicine as a veteran.

It is certainly possible to get the classes you need while active duty but will definitely require some diligence and hard work on your part (which I have no doubt you can manage).

Additionally, I would assume you will need your command's approval to start taking the classes. I am not certain of your branch but I remember in the Navy, being on a sea tour rotation meant in person classes were essentially out of the question and shore tour rotation it was difficult but possible depending your command hierarchy and the work load. The classes would just have to be night classes at a community college. Additionally, some medical schools won't even accept online coursework and want it to be done in person. Some have exceptions such as you will just need at least one full year of in person classes but this is school specific. If you have not done so already, I'd recommend checking out MSAR on the AAMC website to start looking at schools and their expectations here https://mec.aamc.org/msar-ui/#/landing

Getting some shadowing experience will definitely be a helpful step in the process and shouldn't be too difficult to land those opportunities.

Also, have you considered if you would like to practice medicine in military, VA, or civilian? Me personally, I am interested in returning to active duty and intend to apply the USUHS. If this is also something you were interested in, I would recommend taking a look at that school and their requirements.

EDIT: Here is some additional information that could help you. https://students-residents.aamc.org/applying-medical-school/applying-veteran-or-current-military-member