You had 0.01140000 in your 1F8rErCh25PHkPeafBK3eaxpjoVktBdjS3 address in your wallet
You sent 0.001 to bc1q8z68gxl2rl9dy8yh6ve4ugl4q7nl5lurcl53cy
you have 0.0104 btc left out of which 0.00002190 has been used as fees for the tx.
The remainder amount of 0.0103781 has been sent to your change address bc1q4kpyjxmqr7uzcd5w62hc7t273u009tgkjps98p
If you go to bitcoin core, and if you go to settings/wallet and have coin control switched on, go to send bitcoins, on top there you will have an option called inputs. click on it, you will see the address 1F8rErCh25PHkPeafBK3eaxpjoVktBdjS3 with balance 0.0103781 displayed and if you click on it, below another line will open with address bc1q4kpyjxmqr7uzcd5w62hc7t273u009tgkjps98p and change written there with btc amount shown as 0.0103781 .
Next time when you send btc it will be sent from this address. bc1q4kpyjxmqr7uzcd5w62hc7t273u009tgkjps98p
Nothing to worry about at all.
I tried to find this address in my Bitcoin core both sending and receiving address but failed. Is it normal? Should I stop worrying and just continue using my Bitcoin core wallet?
It wont show over there, you will be able to see this address as i have described above.