What makes you think you couldn't become pregnant? Have you seen doctors about it? Or just assumed. Anyways, about your question. If you took a pregnancy test before your period started, (Which I believe you did if your period started on the 23rd and you tested on the 20th) it could have been too soon. When was the last time you had unprotected sex. Generally, you need to allow at least a minimum of 2 weeks from the last sexual encounter to even test, though 4 weeks is the best time to do it. Wait a week, and take another test with first morning urine. You can also make an appointment with a doctor and see if they can do blood work which is more accurate than a standard blood test. Unless you're wanting children, always use protection and birth control.
There is always a chance of being prego. Becoming pregnant is hard in it self. I know we always hear of people haveing sex once time with someone and getting prego but there is more to it. But if you are having unprotected, there is always a chance. As far as your AF coming at different times, It seems like they are coming every month...Stress, Diet, Weight gain/loss, there are several reasons for your AF to be a day late..Now on the other hand, prego women some times bleed while they are prego. I would say to be on the safe side, if you are worried for any reason to seek medical attention. See your GYN or PCP and let them know what is happeneing. If sounds normal to me, but I am not a doc yet. I only know what I have learned this far. But your personal doc would be the best to give you advice. I hope that you get the results that you are looking for.