A.S.
Full disclosure: I am a Chiropractor who has taken care of thousands of children over more than 20 years, including my own child, and very many children and adults with asthma.
Chiropractic can be very helpful for a child with asthma. The neck and upper back area nerve function is intimately related with lung function specifically bronchiole dilation which in basic terms is the ability to take in and release a breathe. In fact, when a person uses a "puffer" they often are trying to replace the chemicals that are normally stimulated by proper nerve function.
My advice is to look for a Chiropractor who sees a lot of children and is comfortable taking on your child as a patient. A recommendation from another parent is often a good place to start and feel free to ask the doctor of Chiropractic any questions you have or express any concerns, but rest assured many children with asthma have been helped with gentle Chiropractic care and there is very nice research backing up the clinical excellence.