I was down on 29th May,13 and has unprotected sex on 20th June and 27th June, 13. After this, I was down on 1st July and now my periods are due but there is no bleeding or any symptoms of having periods. Is there any chance of getting me pregnant? If not, what can be the possible reasons for delayed periods/no periods?

Anytime you have unprotected sex, you take the chance of pregnancy. What do you mean 'you were down... '?
Time for an HPT with first morning urine. If that is not conclusive have a blood test.