I have heard Portuguese Water Dogs are low shedding as well as poodles and bichon friese . Other breeds you may possibly look into would be Maltese, Wheaton Terrier, Afghan, Giant Schnauze. An alternative would be a Chinese crested (like chihuahua in size).
The labradoodle was bred to be a non shedding hypoallergenic dog but alias, some shed and people are allergic to them.
My brother can be around short haired dogs but double coated like the German Shepherd, Akita, Golden Retriever, Huskey he is very allergic to, but he does fine with his blood hound and Beagle.
Everybody’s different and because of your allergies you may not be able to tolerate a dog due to it’s saliva and dander. If you have that many problems around dogs you may want to stay petless.