Double check your dates. There are some problems with them.
You said she should have gotten her period around 18 September but didn't. If so, then no, it's not looking good for you.
If you had sex on September 12 and NOT before, and she expected her period on September 18, it is VERY unlikely that you are the father. The timing is bad for you. She would have ovulated between about September 1 and 6, the egg is only viable for about 48 hours.
It is also VERY unlikely that a pregnancy test would be able to detect pregnancy 7-8 days later. It usually is more like 2 weeks at the earliest, not a week.
Here are the problems:
Her last period would have started around August 21. She wouldn't have needed the plan B then as having sex on the 24th, day 3 of her cycle she likely wouldn't ovulate until day 11 (September 1). Sperm is only viable for about 5 days - until day 8 in this case. No egg, no sperm=not pregnant.
When she stopped taking the birth control pills - if you mean the "active" pills, she should have had an induced period and likely just after the 24th or so...
Was she having sex with him AFTER that? Plan B does NOT provide provide "future" protection against pregnancy.
On the the 12th you said she felt her period coming on. She's not likely to get pregnant during her period.
Hope it helps.
When exactly did her LAST period start? Not the one she missed, her LAST. It should have been near Aug 21, based on a 28 day cycle. Was it NORMAL?
Normally she would have had a withdrawal bleed shortly AFTER she stopped taking birth control. The ECP could have delayed that but it can also cause a withdrawal bleed.
She shouldn't have needed the ECP on the 26th. It's was early for her to conceive.
If she expected her period Sept 18, then it is almost impossible that you, having sex on the 12th, are the father. The egg would not be viable from about September 8 onwards.
The dates are not working out.
You'll need a DNA test to determine paternity.