Hello & welcome,
As you are wearing Braces for orthodontic treatment, gums becoming swollen is common if proper oral hygiene
is not maintained.
Ask you orthodontist to prescribe or dispense any good orthodontic tooth brush along with proper method of using it.
Getting your teeth cleaned by dentist
would also help a lot instead of using any drugs like antibiotics.
One important thing is to get an x-ray done, as it will show if there is any underlying pathology related to tooth or periodontium
related to it so as to get treatment accordingly.
Use of mouthwash prescribed by your dentist for a short period will also help you.
Remember, in orthodontic treatment, patient's role in keeping cleanliness to optimum level is of utmost importance. Always wash your teeth even with gargles after eating food, avoid sticky food stuff as they are difficult to get cleaned once they stick to braces thereby gums become more prone to inflammation & swelling.