Several years ago, I used to have my betta in a 2.5 gallon with a small whisper filter. As he was my first fish and I was just learning, I fed him too much and he developed swim bladder and he got caught in the bottom of my filter. Fortunately I found him fairly quickly and shut down the filter. His fins got pretty torn up which Melafix eventually mended pretty nicely though his tailfin never did totally grow back. I put a divider up until he got over the swim bladder and healed and then I put some sponge at the intake of my filter for precaution sake. As it was a small tank I was not concerned about the filter efficiency. This worked fine. And he lived a long while after this incident.
Not sure that sponge would work for your filter though, especially considering your stock.
Keep an eye on him, maybe he is still settling in.