Everyone reacts to allergens in their own way.
To say yes or no, without a doctor's opinion, is unrealistic.
When cleaning dust, I often get hives on my hands. I don't use chemicals, just a paper towel and water. This may be what you are experiencing.
Bed bugs can also cause a skin rash (hives), but you'll generally find the bites around the same time.
If there are no bites, and this only occurs when you touch or inhale dust, it's very possible.
If it happens when you are cleaning, wear vinyl gloves to avoid contact, and if it's also nasal allergies, you should wear a work mask.
Take an antihistamine when you feel the rash coming on - I do this when I get the tell-tale burning followed by the severe itching.
Don't scratch it, it will make it spread. Make sure you shower in cool water to remove the allergens from your skin.
BTW: I'm also allergic to dust/mites, in addition to a dozen other things. Some cause hives (like dust and bed bug bites) and some don't (like pollen and grass).
Severe allergies and various reactions.