YEs, to apply inside Thailand at Immigration for a conversion of the visa exempt entry or tourist visa into a Non Immigrant O visa based on being over 50 years of age the money (800.000 Thb) needs to come from abroad as a foreign deposit into your own bank account, or double the amount if it is a joint account with the missus.
I guess you have an big stamp from Immigration with the text: Extension of Stay permitted up to 25 May 2022.
If that is the case this permit to stay inside Thailand ended the day you left school, you had to cancel this stamp at your local Immigration Office.
If you did not do this, it means you are in overstay.
A Work Permit is a booklet from the Ministry of Labor that allows you to work at mentioned employer at mentioned address and have nothing to do with your stay in Thailand, there for you need another type of visa and your Non Immigrant ED visa is employment prohibited and can not be used to convert into a Non Immigrant B visa to work.
Only option now is to leave Thailand, apply for the correct visa with documents from your new school and use that visa to come back to Thailand.
Or come to Thailand as tourist to close the gap in time to get documents from the new school.
You visit the local Immigration Office and apply there. It is the decision of the Immigration Officer if you get an extension as being unable to travel.
90 day Extension of Stay based on medical reasons with documents of the hospital.
60 day Extension of Stay based on unable to travel due to Covid
New 30 day Visa Exempt Entry by visiting neighbor countries, be aware that enter into Thailand by many land borders are possible if you meet the Covid requirements, but not leaving to neighbor countries.
If your Embassy provide the Affidavit of Income, you must use it as proof of monthly foreign income. Some Immigration offices want to see bank deposits of this monthly income as proof you actually have and use money to live inside Thailand.