I have never heard of tannins making you sick. Certainly in winemaking they don't make you sick. They actually have a 'health benefit' as antioxidants. <_<
You can always delve into the world of fining. PVPP is very aggressive and will remove most of your tannins, egg white, skim milk, gelatin and issinglass are other options. Some fining agents will work better dependant on tannin length. I often trial pvpp to remove bitter tannins in red wines, (bitterness in wines doesn't come from the same source as in beers) and egg white to remove the more chunky tannins. Skim is good in white wines to help remove phenolics (over extracted skins). More often than not I use a combination to get the desired result.
Easiest thing to do is grab 6 glasses fill them with 50 or 100mL of beer, make up a solution (1 or 10% depending on what you have to measure with, a 200uL auto pippette works well) of whatever agent you choose and then add 10, 20, 40, 60, 80, 100ppm and see which one you like. then add the same ppm to your keg mix through and then either let settle and rack off the clears or filter it.
Always trial a fining addition as you don't want to add more than you need. Finning can also fine out flavour and aroma molecules.
I am pretty sure ross sells PVPP.
Kirk