Swelling near gums can either be due to gum inflammation due to semi erupted wisdom tooth, or infection arising out of a decayed tooth. You have to immediately see a dentist for resolution of your problem. Meanwhile you can do warm salt water gargle for some relief.
It can be gingivitis.
Mostly it is because of either infection due to poor oral hygiene.
Or due to injury because of rough brushing.
Take homoeopathic medicine
carbo veg 30 tds.
While brushing do it gently and in vertical motion.
Take vitamin c.
And use homoeopathic toothpaste heclalva.
Swollen gums discharging pus could either be a tooth infection that is discharging as a sinus, gum boil due to something stuck in gums (eg small fishbone) or localised gum infection due to calculus. Either way, an x-ray of the area will help. As for medication, I will not suggest taking random antibiotics without seeing a dentist first since the problem, if not recognised, will recur. Meanwhile a warm salt water gargle might help ease the pain a little.
Kindly consult a dentist in person for further suggestion. We need more investigations with clinical examination to decide upon treatment. You may need cleaning, root canal treatment & capping. Until then apply clove oil on the decayed tooth. Rinse frequently with mouth wash.
Yes hard brush can damage and cause injury to gums resulting into pain and inflammation. You can apply glycerin, you can gargle with termeric water to reduce pain and inflammation. You can consult me through Lybrate for homoeopathic treatment and further guidance.