A week after a sting, redness, swelling and itching at the site usually means a mild local allergic reaction, not an infection spreading from the bite itself. This pattern is common and generally not dangerous.
Next Steps
A cold compress and an antihistamine tablet can ease the itching and swelling. Keep the area clean and avoid scratching it.
Health Tips
Consult a physician if the swelling keeps growing, turns hot or painful, oozes pus, or you develop fever, since that can mean a skin infection has set in.