I associate short songs with punk rock and 90s indie rock, but classic rock and other genres also have many great short songs. For me the masters of short songs is Guided by Voices check out their albums Alien Lanes and Bee Thousand for many examples. And of course The White Stripes have great short songs. Write in whatever style you want, maybe it’s a pop song or some R&B. This is just a prompt to get you started on a song, if it turns out longer that’s fine.
Here it is warts and all. I recently got a new guitar (mustang copy) and it's got a Kurt Cobain vibe to it so I went with it. Not my usual sound but it was fun. Yesterday I started wanting to scrap this song and start a new one because I was that into it. I'm glad it didn't because there are some nice bits in the song that I like. Maybe I'll revisit this one someday, but tomorrow it's onto the next song.