Hi there, dog allergies are actually caused by dander (the dead skin cells, saliva and urine) of the pet rather than the fur itself. As all dogs produce dander, this means they all have the potential to bring on allergy symptoms, regardless of their breed or type of fur. In light of this, I would be very cautious about letting any dog into your life given both your asthma and allergies.
Regarding the poodle, it may be the case that you weren't around it long enough for it to trigger symptoms – once the dander collects around your home its more likely to bring on an allergic reaction.
If you want more detail about your allergies, you can speak to your doctor.
If you are seriously considering getting a dog, remember that a short visit with it will be less likely to cause symptoms than if you were to bring the dog home. Therefore, you really need a trial period with the dog at home to see if its suitable. A rescue centre will probably be able to advise you better on this.
Do you have questions? Please feel free to ask.
Stay up to date with the latest pollen information by finding your local pollen forecast from over 30,000 locations across the UK.