Hello. The swelling and bleeding you are experiencing is due to the accumulation of plaque and tartar/calculus on your teeth. Plaque and calculus contain a large amount of microorganism which harm your oral hygiene.
You are advised to undergo scaling and polishing (professional teeth cleaning) which would improve the health of your gums, make them firm and reduce the swelling/inflammation.
Kindly visit a periodontist to undergo Scaling and polishing.
Health Tips
Maintain proper oral hygiene, Brush twice a day using the correct brushing technique. Use a floss. Gargle after every meal.