I am confusing myself with the gender stuff... It's really confusing if you are not used to it!

This is a very simple question but suddenly I feel unsure... !

Я должен ему позвонить вечером.
(is должен relating to "ему" or "я" ....? If the speaker is a woman, could she say this, because she is referring to a man? Or should she say "должна" because she is a woman...?

Same thing with this sentence. A man says:
"Я думаю что моей жене нужен врач".
I know this is correct because it's from an example sentence... нужен refers to the doctor and not the wife. But this was confusing at first and it's easy to think that it should be "нужна" because it's a woman that needs something. Hmmmm....