İs a external hemorrhoid incision considered surgery? TMI!

TMİ. I had a thrombosed hemorrhoid and the doctor said I need surgery. So they numbed it with a local anesthia, cut it open and drained the bloods clots out is this even considered surgery? Its been 3 days I do sometimes get a burning and stinging sensation. They put me on antibiotics, anusol and some antibacterial liquid that they use after operations. I didnt even think this was considered surgery as they wanted a lot of money after the process that took like 15 minutes.