I'm sorry to tell you, but your setup won't really filter out the dust that's making you cough. It's the fine stuff that causes the problems, and they will go right through those filters.
As Gary mentioned, a good cylcone is a useful addition to a good dust collection system, but it's not the only part.
We make a lot of dust. Over the years, I've fought dust collection and tried many different things. Most of which didn't work as well as I'd hoped they would.
Here's the cliff notes version of what I've come up with:
1. Collect all dust and chips that you can at the point of creation. Use hoods and router boxes and lots of air flow. Air flow is huge! You have to have enough to keep the fine dust from escaping and enough to keep the bigger chips in suspension.
2. Use a really good cyclone. The cyclone will separate the chips out so they don't plug up your filters. A really good cyclone will also separate much of the fine dust, keeping it from plugging your filters.
3. Use high quality filters. Down to microns! They're not cheap, but if you keep a good cyclone running they won't plug up too fast.
Obviously, not everyone creates as much dust as we do. However, everyone should take the steps necessary to control the fine dust in their shop. It's bad for you, and the stuff gets everywhere!
Good reading:
http://billpentz.com/