The answer is: it depends...
Some school will have you sign an agreement at the beginning of your first year that you agree not to work during medical school. At others, it is at your discretion whether you want to work or not, but the study schedule is brutal enough that, unless you have a easy job, where you spend most of your time studying anyways, working becomes out of the question.
Third and fourth year rotations run consecutively, so you don't have the time to work. Whatever free time is built into your schedule you will be using it for your residency interviews.
Some of my classmates work at our study hall, which gives them the chance to study while they are at work. Someone has a one intensive weekend a month job. The majority doesn't work though.
As for working in health related fields, some schools will make you sign an agreement that you will not do so (no matter whether you are a licensed professional in that field, such as nurses or PAs), without the authorization of the school. This is done to prevent instances where you may find yourself suspected of practicing medicine without a license.
Don't make a commitment to work before you start medical school, nor count on work income to help pay your way through. Plan on relying exclusively on loans to begin with and then see how you feel about working after you have been in school for a couple of months and what the policies of your school are in this area.
