Covid Positive doubts. 1st symptoms?

We had hospitalized my father for different reason, so that I was travelling to home and hospital for about 10 days. After discharging my father, in 2 days time my brother and I had some symptoms on 14/04/2021, headache, tiredness, body weakness & chest cold. My brother had fever too. Apparently had some weird taste and smell. We didn't undergo any testing & took some some home remedies, since we had very mild things that we are capable to do daily chores. We have recovered from it by 27/04/2021. So, it was puzzle for me about this health issue of mine. And on Thursday, there was covid test camp, where I gave sample for testing. On Monday they called and informed my result is positive. Right now, I don't have any symptoms & family members are doing well. Am confused, whether there is a chance to test postive after 23 days from 1st symptoms? Please Clarify it. FYI Now, Its 6 days since I gave test.