How long does it take swelling to go down after #6 tooth extraction? i also had an infection in it to begin with and was prescribed no antibiotics?

Not sure why you weren't prescribed antibiotics, but it can take a week or so to resolve without. A shame to lose # 6 at such a young age, one of the strongest teeth in your mouth.

Swelling will go down faster if you ask for antibiotics. If you keep area clean and take antibiotics, swelling will go down in less than a week.

To many variables to list here. Short answer, resolution of swelling determined by severity of infection, length of time it went untreated, and your own physiology. Follow your Dentist's instructions to the letter. If you have concerns, he/she is responsible for your post-surgical care.