Hi there.
I can't help with the axie being sick, sorry, but I have a couple ideas about the filter as I had similar problems, that might help at least so you can run it at night? Sorry if this is totally useless info, as I'm a new axie owner, but it took me about 3 months to notice this with my filter.
I don't know what kind of filter you have, but for mine, I noticed that the lower the water was in the tank, the louder the filter was, and the higher the water level, the quieter. The difference is huge, at least with my filter, and makes more noise difference than I thought was possible. So if your tank water level is lower than the filter settings recommend, it might help?
I've also noticed a small fan can drown out the noise quite nicely, although I don't know if this will help your poor bird with his night terrors.