Here is another question. How much does your mom want a dog, and how committed is she to making this work?
I've already mentioned my supervisor who died of asthma. He didn't particularly like cats, but he liked his girlfriend. Among the many fatal mistakes he made was to simply try to avoid the cats and put it all on his girlfriend to deal with them.
I had another supervisor who also had asthma, who loved animals, and who was determined to keep animals in his life. He was very active in managing his allergies and getting help in reducing his exposure to allergens. He bathed his dogs and cats weekly. His girlfriend brushed the animals between baths. He installed hardwood floors. He hired a cleaning service to damp dust and HEPA vacuum his house weekly. He switched to using a duvet with a washable cover, which his girlfriend washed weekly (along with doing all the rest of their laundry.) He met regularly with an allergist to get his medications adjusted. Managing it all was a huge effort on his part - and his girlfriend too - but it allowed him to control his asthma enough to keep his pets while avoiding scary incidents.