Your last regular period STARTED June 18. You'd normally ovulate between days 11-16 of you schedule. Sperm can survive up to about 5 days. You had sex on day 4 of your cycle, very early. It's unlikely but not impossible that you'd get pregnant. However, you took Plan B. That makes it even more unlikely that you were pregnant then.
Plan B does NOT provide "future" protection.
You had possible period on the July 2.
You had sex on July 17, 17, and 19.
The problem with trying to calculate the timing is that the Plan B can make your cycle "off schedule." Assuming what you had was a period on July 2, you had sex on days 15, 16, and 17 of your cycle. Normally you'd ovulate between days 11-16 of your cycle and the egg is viable for about 48 hours.
Translation, you likely had sex near your peak fertility and used NO protection.
It's very likely that the July 17-19 guy is the father. Although the Clear Blue date of conception "works" remember that it is just an approximation.
A DNA test can confirm paternity. They can be done before birth.
Hope it helps. Good luck.