Ask an Immigration Solicitor. Get an Answer ASAP.
I am a solicitor.
You should not worry. There is a grace period of up to 14 days, please see this guidance from the Home Office:
"First, overstaying will be disregarded if the Secretary of State considers that there was a good reason beyond the control of the applicant or their representative, provided in or with the application, why it could not be made in time, provided that the application is made within 14 days of the expiry of leave."
As you have a good reason why you applied a day later, you should be fine and you should not worry. You should simply await the outcome of your application.
May I help further?
Once you have put in your application, you are entitled to wait until it is decided. You would not be an overstayer as you have a pending application within 14 days of the grace period.
The explanation is fine, even though you gave it after applying.
You should not worry.
All the best
It could be up to 12 weeks.