When you say a character shook their head, does that mean they nodded, as in "yes", or they shook it sideways, signifying the answer is "no?"
From personal experience (central Europe) I would say that shaking your head is normally a "No" and nodding your head is normally a "Yes". But looking through English.SE: When moving one's head to answer a question does “nod” mean yes and “shake” mean no?:
Head movements vary in their meaning depending on the culture in question. In general, in countries where English is the native language, a "nod" (not a "node") is an up and down movement of the head meaning "yes." A head shake is a side to side movement meaning "no." At least for most English speakers in Britain and America, a nod never means no, and a shake never means yes. This is somewhat oversimplified and variations exist, but for the most part, the basic pattern is as I have stated it.
As a writer you should make sure that there are other clues for the reader to show what the intention is. For example you could add that the character is "shaking their head in disagreement" or "nodding enthusiastically".
As stated, a "shake" of the head is the side to side movement, a nod is up and down, and a bob of the head is down then up.
Generally speaking a nod means yes and a shake means no.
But then it gets complicated. Because a shake doesn't always indicate a negative emotion or a negative reaction. A small shake of the head with a small smile can indicate humour, or self depreciation, or a reaction to a bad joke. Fast movement side to side can be used to "refresh" someone, wake them up. It can mean disagreement with the speaker, or it can be used in support of a statement made by the speaker. It can indicate denial, rejection, refutation, disdain, anger, support and myriad other emotions and actions.
With a shake of the head, body language, context and environment matter before we even begin to get into cultural/geographic variances. Especially in places like Australia where phrases like "Yeah, nah" and "Yeah, nah, yeah" are proudly uttered and confuse non-Australians endlessly. Where depending on the position in the sentence, expletives can either be negative and abusive, or a term of endearment.
For me it works like this.
A nod is primarily a signal of positive empathy. A shake is primarily a signal of negative empathy.
If someone says something good and you want to confirm that, you nod. If someone says something good and you want to deny that that, you shake your head.
If someone says something bad/horrible and you want to confirm that you shake your head. If someone says something bad/horrible and you want to deny that, you distance your self by not giving any feedback.
Also a popular acronym: Urban Dictionary: smh
Acronym for 'shake my head' or 'shaking my head.' Usually used when someone finds something so stupid, no words can do it justice. Sometimes it's modified to 'smfh' or 'smmfh' by those that prefer profanity in their internet acronyms. trick1: i got a headache...i hit myself in the head with my knee while trying to do situps.
Basically shaking ones head at a loss for words or in utter disbelief. Hardly likely to mean yes.