Possible Pregnancy

I need an opinion...

My last period came earlier than expected (I’m on the pill) and stopped the typical 5 days. I couldn’t start a new pack because insurance wouldn’t allow me to get a new one, so I started my pill pack 7 days after the last day of my period (Aug 3rd)

Now we weren’t using protection and it didn’t dawn on me until I started having potential early signs of pregnancy this week that I wasn’t covered.

Am I crazy for thinking I am possibly pregnant?? I’ve never messed up my pills this badly.

If it is possible, when could I test? My period should (by cycle length) be due on Aug 20th but by pill pack it’s not due until Aug 23rd.