Gum disease or periodontal disease can happen in teeth when the hygiene is not maintained properly. As.a general advice after braces particularly fixed braces we instruct the patients to brush with a specialized orthodontic tooth brush, interdental cleaning and flossing and regular mouth wash. This is apart from their regular periodic visits to the dentist. When any appliance is worn in the mouth the care to the teeth, gums and surrounding structures must be 200% more than a normal individual.

Braces/orthodontic treatment as such does not cause gum disease /periodontal disease.  However,  it may be a factor in retention of food particles which can cause inflammation  in gingiva(gums).  If not treated early enough it may cause gingiva enlargement /periodontal disease. Therefore,  it's must to have an impeccable oral hygiene.  Since you have got scaling  done already and started antibiotics  as directed  by your dentist,  it should start settling.