You can continue showing your GP because the medications prescribed are the standard ones. But, I will advise you to visit a specialist atleast once in a year.
My opinion as a mom to 2 asthmatic children who are now 18, 16 is a definite YES. GP's are great to maintain, but specialists we have found are better at getting to the maintenance point thru PFT tests and further specialization/knowledge.
Just my thoughts on it and Welcome to our Community!
C~