If you can tolerate a mouth guard it will help.
It's not swelling (but it feels like swelling), it's the muscles becoming floppy and the inside of the mouth doesn't hold shape so well. Also there can be some spasticity, which causes muscles not to move so smoothly and so biting inside the mouth incidents increase.
I remember in the early days, during the months of trying to get a diagnosis, as bulbar onset, Chris would tell me and every doctor that inside his mouth was swollen, he could feel it. They would all assure him it was not.
We finally figured out what was going on. However a mouth guard caused him to salivate copiously and gag.
The biting inside the mouth is really cruel, I hope someone else found another way to help stop it.