Periods aren't an exact science, unfortunately, especially when it comes to their timing. Before I look at your specific dates in relation to pregnancy, I want you to pull up a calendar for April 2018, and we're going to go over some hypothetical dates.
Let's say your period comes on April 1st, 2018 and you have a 28-day cycle (this is the average and most typical length of time that a woman's cycle lasts). You would get your period 28 days after April 1st, which is April 29th. Not only would you get two periods in one month, but the first period would also be at the beginning of the month and the second period would be at the end of the month. Confusing, but not at all irregular and in fact this is the clinical example of a "typical" period. Now let's say your second period is just two days late - you would begin that second period on May 1st, putting your period back into the first week of the month.
A good way for you to see just how regular or irregular your periods are is to use a period tracking app. I like Flo; it lets you track a lot of other stuff too.
Now, to your pregnancy question - since I don't know how long your average cycle lasts, I can't make an educated guess on when you probably ovulated. But, going off from a typical cycle, I think March 1st would have been too early for you to get pregnant unless you ovulated quite early. The most likely days for your ovulation and the highest chances of conception were probably around March 7th through the 11th.
All of that being said, you can check out the pregnancy test calculator for yourself at CountDownToPregnancy(dot)com where you can put in the start date of your last period (February 23rd) and then put in the average length of your cycle to find out when you should start testing for pregnancy. Personally, I think the best day for you to test would be on March 24th. This would be day 29 of your cycle, and unless you have very long cycles, you'd probably get an accurate result.