I started my career as a bread baker and then moved to pastry working many early morning hours and long days amid huge bins of flour and such. Being slightly asthmatic, I didn't have too much of a problem, though it seemed that I always had a mild case of bronchitis.
Once I moved away from a flour-filled atmosphere, it got better, but in the main kitchen, air borne grease and oil particles were still a problem.
Garde Manger was much better, though I didn't like it as much.
Now I have a son who has very bad asthma. When he was younger, we had to rush him the ER 3-4 times a year because he just couldn't breathe. Knowing how sensitive he is to airborne dust, pollens, mold spores and such and how severe the attacks were that these particles trigger, I would advise you against pursuing professional baking without having a serious talk with your doctor and probably a pulmonologist too.
If your heart is set on it, they can probably advise you on the best way to avoid triggers and devise strategies to keep your lungs healthy.
Keep in mind that baking at home is a whole different animal than baking in a large volume professional bakery. Every time you dump a 50 pound sack of flour into a storage bin, you get a dusting. Same with sugar. You will come home with flour in your nose, ears, hair, clothes and caked on your skin and under your fingernails.