Can you be allergic to a hypoallergenic dogs?

So lately Iv been getting "hives", it comes and goes really, it's been a week or so now in witch it has gotten worse, around a month ago i used to get them all over my body, id wake up itching like crazy in the middle of the night, my mom says it's probably cause i was eating to many eggs, they say you should eat only two a day, i was sort of livin' on eggs, anyways i stopped that, and i got better, but now it has gotten worse, i just got sent home from school because the teachers were concerned.. i was just wondering, can you be allergic to a hypoallergenic dog? we bought a puppy 2-3 months ago, a bichon/poodle mix, i was just fine in the beginning, and iv had dogs my whole entire life, do you think i could be allergic to my puppy? if yes, what can i do to stop this allergy, is there a way? cause im not giving my puppy away : ( help?