Most of the following comes from the article: Punkpunk: A Compendium of Literary Punk Genres
First of all, appending "punk" at the end is often used to show that the main character or characters belong to a certain niche group and are rebelling against the current society - the defining aspect of which is in these cases the technology. Anything that is categorized as "-punk" can therefore be said to focus on the technological aspects of a society and illustrate the problems that arise from excessive usage of such technology, whether from a personal or a societal standpoint.
There are lots of different genres that belong to this "-punk" group and you can categorize all of them under "retro-futurism" or "sci-fi-punk".
Here is a list of genres taken from the mentioned site and shortened:
- cyberpunk: started the trend; future dystopia; humanity and technology become one
- steampunk: past (victorian era) dystopia; technology is usually steam-powered
- dieselpunk: World War I or World War II; big machines and black smoke
- biopunk: cyberpunk, but with a focus on biology, such as implants and DNA hacking
- bugpunk: biopunk, but only with bugs...
- transistorpunk: Cold War
- nanopunk: cyberpunk, but only with nanotechnology
- decopunk: dieselpunk, but with Art Deco style...
- atompunk: shortly after World War II
From then on it's getting pretty ridiculous (the author says this themselves), but:
- clockpunk: Like steampunk, but in the time of Leonardo Da Vinci
According to Wikipedia Leonardo lived towards the end of the medieval age. At least close by. "Medieval" can mean anything from the 6th to the 15th century and Leonardo was born 1452, so it's not unreasonable to say that your genre is in fact clockpunk.