I realise this post is a bit old and hopefully you will have got something sorted by now. I've been allergic to house dust mites practically all my life (actually its the proteins in their droppings that cause the allergy) and most likely in my case, sensitivity is due to a genetic thing as my mother was allergic to other things as well (in later years I developed hay fever when I was 35 and asthma at 40) As you say you already suffer from asthma, it is probably a similar immune reaction.
Keeping the dust down is probably the only thing you can do - I always use a damp cloth to wipe things down with and never used a dry duster. Also, give the carpet, upholstery and curtains a good clean (steam clean if you can - protein is degraded at temperatures above 60oC) and there are anti-allergenic products on the market that you can use instead of the usual detergents. Thereafter, a hoover with a good filter (also known as HEPA filter) as per your usual cleaning regime. If the mattress and pillows are getting on a bit, perhaps it may be worth replacing them otherwise the alternate especially the mattress, would be to put a cover over it (I'd like to say plastic sheet but I think there are things you can use - have a word with your local pharmacist for products that are available)
As for the pets, they can still produce the dander and skin flakes (dust) which the house dust mite feeds on - so indirectly, they can contribute to the problem especially their bedding so don't forget to give that a good washing/cleaning too.
albertajune wrote:I have just been told that I am allergic to house dust mites. I can't look at a picture of them anymore!
All houses have a thriving colony of different mites and other little insects, even the cleanest, so please don't feel it is a reflection of your home LOL