Dog allergy

a little backstory, we previously had a small shih szu for 3 years until he was ran over. we then adopted a st benard puppy maybe 4 months afterwards. 2 weeks into getting her, my son started with a cough. 2 weeks later took him to the dr and they said it was just respiratory illness. cough was the only thing he had BTW. fast forward 2 months later, he still has the cough. I have to give him Loratidine for it to go away. not sure how to go about this, he’s 6. and before the Karen’s come in here saying just rehome the pet, she’s made a impact on us in such a short period of time, but I understand my son can’t be on allergy medication forever..