Is there a succinct word for the 'itch' to do something creative? For example having a niggle in your brain where only doing something creative can make it go away?
While it isn't a single word, the phrase creative frenzy is often heard. By itself, frenzy means
A state or period of uncontrolled excitement or wild behavior [Oxford Dictionary Online]
Other similar terms are creative fervor and creative fever.
fervor: great intensity of feeling or belief; ardour; zeal [Collins]
fever: A state of nervous excitement or agitation [Oxford Dictionary Online]
The terms could be used by themselves if the context reflected the source of the agitation, as in
He was in a frenzy that only a full day of writing could relieve.