You say your period is due around 16th june?
Assuming that you have a normal cycle of 28 days...
Would make your last period about 20th may and ovulation about 2nd june.
26th may (when the condom broke) is about 7 days before ovualtion.
So to conclude the risk of pregnancy is very low but still a risk.
Your "high fertility" is from 5 days before ovulation until 2 days after.
This doesn't mean other times are "safe" just that the risk is lower.
(unless you chart your: bbt, cycles, cm, etc with absolute accuracy and know when you ovulate exactly)