I’ve noticed that when you talk about someone doing a job, you don’t use an article. For example, « il est prof » and not « il est un prof ». I’ve also noticed in a French movie how a woman said « je suis femme » rather than « je suis une femme ». Is there a rule for this situation, and how strict is it when it comes to when you can use it?

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You are right, this is a special rule that says that we do not put article in front of job, because it is grammatically considered as an adjective when it is used alone :

1. « Martin a beaucoup étudié, il est maintenant médecin. »
2. « Elle est expert-comptable. »

The rule changes if you add an adjective or a complement to the job :
« Martin a beaucoup étudié, il est maintenant un médecin de renom. »
« Elle est l’expert-comptable de ma compagnie. »

This rule is an exception, in all the other cases, we need to put the article like in your sentence : « Je suis une femme ».

If hope my explanation was clear enough !