What is the difference between the filter on my furnace and an Air Exchanger?
Do you mean HRV/ERV? They won't help with allergens. In fact they are likely to make the situation worse. Their job is to bring in fresh air and pre condition it with the outgoing air. They do have filters but they are just to protect the exchange core. If your allergic reactions are due to pollen and the like an HRV will make it worse as the equipped filter is not a MERV rated filter. You would be better off installing a whole house HEPA unit.

Duct mount HEPA



Elecro-Air Five Seasons

I've installed lots of these. You would leave the furnace fan running constantly as well as the HEPA filter fan. There are much better options available from IQAir but they are very expensive.