I recently experienced a patch where in I just had an urge to write and write. And when I sat down on my laptop, indeed I went on and on writing things I always wanted to. I felt like I experienced something that is opposite of writer's block. Is this a thing? Is there a term in English for this?
Yes, it's a thing. It's called flow. In the book Quiet: The Power of Introverts in a World That Can't Stop Talking, the author, Susan Cain, writes:
Flow is an optimal state in which you feel totally engaged in an activity—whether long-distance swimming or songwriting, sumo wrestling or sex. In a state of flow, you're neither bored nor anxious, and you don't question your own adequacy. Hours pass without your noticing. The key to flow is to pursue an activity for its own sake, not for the rewards it brings...
[According to influential psychologist Mihaly Csikszentmihalyi,] in flow, "a person could work around the clock for days on end, for no better reason than to keep on working."
Zoning is a term sometimes used for this. The wikipedia flow article mentions several related terms: in the moment, present, in the zone, on a roll, wired in, in the groove, on fire, in tune, centered, and singularly focused. I've heard or read all of these used in the required sense, except for the last one; and the first one, in the moment, I usually think of as meaning fully aware of what's going on, rather than being in the zone. Some other terms used to describe the flow-state are up, on, and channeling. [Eg: “When it is my turn to sing karaoke, I am going to channel Ray Charles.” - wiktionary]
Perhaps a writing jag. American Heritage defines jag as
A period of overindulgence in an activity; a spree: a shopping jag; a crying jag
Collins defines it as
a period of uncontrolled activity
An alternative is a writing binge. Cambridge defines binge as
an occasion when an activity is done in an extreme way, esp. eating, drinking, or spending money: He admits to having an occasional ice-cream binge.