A skin prick test is really the only definitive way to diagnose allergies to dust and to anything else, for that matter. Otherwise, how could you tell if it was dust or mold, for instance? And a faceful of dust will make anyone sneeze just from the mechanical reaction, so that is not indicative.
But you should ask whether the skin prick test is worthwhile. There are two main things you can do more effectively afterwards than before: get allergy shots (immunotherapy) and make lifestyle changes to avoid your allergen. For instance, if you *are* allergic to dust mites, you could make your bedroom a dust-free zone - but be warned, this is a *big* commitment. If your allergies are minor and just require the occasional dose of medication, you might decide that testing is not worthwhile.