When alternator belt broke car over heated

yes when the alternator belt breaks it will overheat.

There is now a noise coming from what I believe is the timing belt area, not sure if I should drive it to the repair shop

it depends on how loud it is if it's a ticking then maybe but if you are worried about it then get it towed

Well any ideas what could cause the noise after something like this happens?

if it sounds like the timing chain area i'd have to say something went wrong in there. like maybe a tensioner broke, etc. without hearing it and on computer you can't this is really a shot in the dark. it's possible it could be something with the water pump because it would stop turning when the belt broke.

It kind of sounds like something slapping if that helps any

i'd suspect a chain then

Is that expensive to fix

depending on where you are i'd imagine around $1000 but get a quote as it may not be that. It cold be more depending on where you are.