The allergy problem is probably caused by the filter not working rather than the ionizer feature.
Ionizers are throwing out 'negative' ions, meaning they carry some extra electrons. This is the same effect as you get when it rains. The falling rain generates 'static' electricity (which is why rain is often accompanied by lightning) and charges the air. One effect of this is to 'capture' lots of dust and finer particles in the air. In the Great Outdoors all this means is 'fresh air' but
indoors it means dust & odors clinging to walls, furniture, and everything else as those charged ions carrying all that dust have to go somewhere. Outdoors it doesn't matter if they stick to the trees & ground of course.
CRTs and many other electronic parts throw off a lot of
positive ions, btw. Which means that the negative ions tend to be attracted to electronics, and can clog up your electronics much faster than would normally occur. Ionizers are hard on electronics. So it's entirely possible that the dust is coming to meet you as you sit in front of your computer.
That could also be why the room seems 'worse' with the ionizer.