Hi. At home pregnancy tests are pretty accurate. They are typically only wrong when used incorrectly, testing too early, read too soon, etc. You should be able to get a positive test if pregnant 2.5 weeks after the sex you are worried about that may have gotten you pregnant.
You can get pregnant from the pull out method. So, wait until it is 2.5 weeks after the sex and then trust the negative test.
Most women will have a late period (or long cycle which it really is) from one time to another even if it is not their norm. It happens due to changes in routine, illness, stress, trauma, weight gain or loss, etc.
good luck